tag:blogger.com,1999:blog-22569988696763245112024-02-06T19:18:14.081-08:00AL410 - Algebra CommutativaA.A. 2016-2017Unknownnoreply@blogger.comBlogger1125tag:blogger.com,1999:blog-2256998869676324511.post-64148310342178464202017-01-06T12:00:00.000-08:002017-01-06T07:20:16.702-08:00<div dir="ltr" style="text-align: left;" trbidi="on">
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<b style="background-color: #a9cde8; color: #660000; font-family: arial;">Docente: Marco Fontana</b><span style="color: #660000; font-family: "arial";"> </span></div>
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<span style="background-color: #a9cde8; color: #660000; font-family: "arial";">Dipartimento di Matematica e Fisica, </span><br />
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<span style="color: #660000; font-family: "arial";">Orario di ricevimento (</span><span style="color: #660000; font-family: "arial";">I Semestre 2016/17):</span></div>
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<span style="color: #660000; font-family: "arial";">Martedì ore 10-11 e Giovedì ore 13-14</span></div>
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<i style="color: #660000; font-family: arial;">oppure</i></div>
<span style="color: #660000; font-family: "arial";">per appuntamento da fissare via ema</span><span style="color: #660000; font-family: "arial";">il </span><span style="color: #660000; font-family: "arial";"> </span></div>
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<span style="color: #660000;"><b><span style="font-family: "arial";">Scheda del corso (Syllabus per il Diploma Supplement)</span></b><span style="font-family: "arial";"><o:p></o:p></span></span></div>
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<span style="color: #660000;"><span style="font-family: "arial";">Moduli. Ideali. Anelli e moduli di frazioni. Anelli locali. Anelli e moduli noetheriani. Teorema della base (BasisSatz) di Hilbert. Dipendenza integrale. Anelli di <span style="background-color: white;">valutazione</span>. Teorema di Krull (chiusura integrale e valutazioni). Teorema degli zeri (NullstellenSatz) di Hilbert. Domini di Dedekind. Anelli e moduli artiniani. Spettro primo di un anello e topologia di Zariski.</span><span style="font-family: "arial";"><o:p></o:p></span></span></div>
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<span style="color: #660000;"><span style="font-family: "arial";"><i>Ulteriori argomenti potranno essere svolti in accordo con gli studenti frequentanti.</i><br />
<i> Il corso è rivolto agli studenti della laurea triennale e magistrale ed è particolarmente indicato per coloro che intendano approfondire tematiche di algebra, geometria algebrica e teoria dei numeri.</i><br />
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<span style="color: #660000;"><b><span style="font-family: "arial";"> Crediti (CFU-ECTS): 7 I Semestre </span></b><span style="font-family: "arial";"> <b>Prerequisiti: </b>AL210 </span><span style="font-family: "arial";"><o:p></o:p></span></span></div>
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<span style="color: #660000;"><i><span style="font-family: "arial";">Insegnamento valido per la PFA (Prova Finale di tipo A)</span></i><span style="font-family: "arial";"><o:p></o:p></span></span><br />
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</span></i></span> <span style="color: #660000;"><span style="font-family: "arial";"><b>orario:</b> Martedì e Giovedì ore 11-13, Aula 211; </span></span><br />
<span style="color: #660000;"><span style="font-family: "arial";">Lunedì (Seminario Studenti) ore 14-15, Aula 311 </span></span></div>
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<span style="color: #660000;"><b><span style="font-family: "arial";">Bibliografia essenziale</span></b><span style="font-family: "arial";"><o:p></o:p></span></span></div>
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<li class="MsoNormal"><span style="color: #660000;"><span style="color: #660000; font-family: "arial"; mso-fareast-font-family: "Times New Roman";">M.F. Atiyah - I.G. Macdonald, Introduction to commutative algebra, Addison-Wesley, 1969. Edizione in italiano con note di P.Maroscia, Feltrinelli, 1981.</span><span style="font-family: "arial"; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></span></li>
<li class="MsoNormal"><span style="color: #660000; font-family: "arial"; mso-fareast-font-family: "Times New Roman";">I. Kaplansky, Commutative rings (revised edition), The University of Chicago Press, Chicago, 1974.</span></li>
<li class="MsoNormal"><span style="color: #660000;"><span style="color: #660000; font-family: "arial"; mso-fareast-font-family: "Times New Roman";">H. Li, An introduction to commutative algebra (from the viewpoint of normalization), Word Scientific Publishing Company, 2004.</span><span style="font-family: "arial"; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></span></li>
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<span style="color: #660000;"><b><span style="font-family: "arial";">Ulteriori riferimenti bibliografici</span></b><span style="font-family: "arial";"><o:p></o:p></span></span></div>
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<li class="MsoNormal"><span style="color: #660000;"><span style="color: #660000; font-family: "arial"; mso-fareast-font-family: "Times New Roman";">Nicolas Bourbaki, Algèbre Commutative, Chapitres 1-9, Hermann, Paris, 1961 ....</span><span style="font-family: "arial"; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></span></li>
<li class="MsoNormal"><span style="color: #660000;"><span style="color: #660000; font-family: "arial"; mso-fareast-font-family: "Times New Roman";">Arthur Chatters, C. R. Hajarnavis, Charudatta Hajarnavis, An Introductory Course in Commutative Algebra, Oxford Univ Press, 1998.</span><span style="font-family: "arial"; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></span></li>
<li class="MsoNormal"><span style="color: #660000;"><span style="color: #660000; font-family: "arial"; mso-fareast-font-family: "Times New Roman";">David A. Cox, John B. Little, Donal O'Shea, Ideals, Varieties, And Algorithms: An Introduction to Computational Algebraic Geometry And Commutative Algebra, Springer Verlag, 2007.</span><span style="font-family: "arial"; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></span></li>
<li class="MsoNormal"><span style="color: #660000;"><span style="color: #660000; font-family: "arial"; mso-fareast-font-family: "Times New Roman";">D. Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry. Springer, 1995.</span><span style="font-family: "arial"; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></span></li>
<li class="MsoNormal"><span style="color: #660000; font-family: "arial"; mso-fareast-font-family: "Times New Roman";">R. Gilmer, Multiplicative Ideal theory, Dekker, New York, 1972.</span></li>
<li class="MsoNormal"><span style="color: #660000;"><span style="color: #660000; font-family: "arial"; mso-fareast-font-family: "Times New Roman";">Manfred Knebusch, Digen Zhang, Manis Valuations and Prufer Extensions I: A New Chapter in Commutative Algebra, Springer 2002.</span><span style="font-family: "arial"; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></span></li>
<li class="MsoNormal"><span style="color: #660000;"><span style="color: #660000; font-family: "arial"; mso-fareast-font-family: "Times New Roman";">E. Kunz, Introduction to Commutative Algebra and Algebraic Geometry, Bikhauser, Berlin, 1985.</span><span style="font-family: "arial"; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></span></li>
<li class="MsoNormal"><span style="color: #660000;"><span style="color: #660000; font-family: "arial"; mso-fareast-font-family: "Times New Roman";">H. Matsumura, Commutative Algebra,W. A. Benjamin, 1970.</span><span style="font-family: "arial"; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></span></li>
<li class="MsoNormal"><span style="color: #660000;"><span style="color: #660000; font-family: "arial"; mso-fareast-font-family: "Times New Roman";">H. Matsumura, Commutative Ring Theory, Cambridge University Press, 1989.</span><span style="font-family: "arial"; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></span></li>
<li class="MsoNormal"><span style="color: #660000;"><span style="color: #660000; font-family: "arial"; mso-fareast-font-family: "Times New Roman";">M. Reid, Undergraduate commutative algebra, LMS Student Texts, Cambridge 1995.</span><span style="font-family: "arial"; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></span></li>
<li class="MsoNormal"><span style="color: #660000;"><span style="color: #660000; font-family: "arial"; mso-fareast-font-family: "Times New Roman";">R.Y. Sharp, Steps in commutative algebra, London Mathematical Society Student Texts, Cambridge University Press, Cambridge, 1990.</span><span style="font-family: "arial"; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></span></li>
<li class="MsoNormal"><span style="color: #660000;"><span style="color: #660000; font-family: "arial"; mso-fareast-font-family: "Times New Roman";">I. Swanson, C. Huneke: Integral closure of ideals, rings, and modules. Cambridge Univ. Press, 2006.</span><span style="font-family: "arial"; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></span></li>
<li class="MsoNormal"><span style="color: #660000;"><span style="color: #660000; font-family: "arial"; mso-fareast-font-family: "Times New Roman";">John J. Watkins, Topics in Commutative Ring Theory, Princeton University Press, 2007.</span><span style="font-family: "arial"; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></span></li>
<li class="MsoNormal"><span style="color: #660000;"><span style="color: #660000; font-family: "arial"; mso-fareast-font-family: "Times New Roman";">O. Zariski and P. Samuel, Commutative Algebra, Van Nostrand, 1958-1960 (reprinted, Springer 1975-1977)</span><span style="font-family: "arial"; mso-fareast-font-family: "Times New Roman";"><o:p></o:p></span></span></li>
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<span style="color: #660000;"><span style="color: #660000; font-family: "arial";"> <b>Appunti on-line di corsi di introduzione all’algebra commutativa</b> <b>ed altri links utili</b> </span><span style="font-family: "arial";"><o:p></o:p></span></span></div>
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<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"><b><a href="http://www.mat.uniroma3.it/users/fontana/documents/clarck-commutative%20algebra.pdf" target="_blank"><span style="color: #660000;">Pete L. Clark (U. Georgia, Athens): Commutative Algebra </span><span style="color: blue;"><span style="background-color: red; color: white;">.pdf </span></span></a></b></span><br />
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</span></b></span><span style="font-family: "arial" , "helvetica" , sans-serif;"><b><span style="color: blue;"><a href="http://www.maths.nott.ac.uk/personal/ibf/courses.html">I. Fesenko: Commutative algebra</a> >></span><span style="color: #660000;"> </span></b><o:p></o:p></span></span></div>
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<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"><span style="color: #660000;"><i style="color: #660000;">This course is an introduction to modules over rings, Noetherian modules, unique factorization domain and polynomial rings over them, modules over principal ideal domains, localization</i><span style="color: #660000;"> </span><a href="http://www.maths.nott.ac.uk/personal/ibf/als3/leno.pdf"><span style="color: blue;"><span style="color: #660000;">[</span><span style="background-color: red; color: white;"><b> pdf </b></span><span style="color: #660000;"> file 202K]</span></span></a><span style="color: #660000;">.</span></span><span style="color: #660000;"><o:p></o:p></span></span><br />
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<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"><b><span style="color: blue;"><a href="http://www.math.uiuc.edu/~r-ash/ComAlg.html">R.B. Ash: A course in commutative algebra</a> >></span></b><o:p></o:p></span></div>
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<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"><i><span style="color: #660000;">Chapter 0 Ring Theory Background (7 pp.); Chapter 1 Primary Decomposition and Associated Primes (15 pp.); Chapter 2 Integral Extensions (9 pp.); Chapter 3 Valuation Rings (9 pp.); Chapter 4 Completion (10 pp.); Chapter 5 Dimension Theory (15 pp.); Chapter 6 Depth (4 pp.); Chapter 7 Homological Methods (8 pp.); Chapter 8 Regular Local Rings (3 pp.; ) Exercises (7 pp.); Solutions (8 pp.); List of Symbols; Index</span></i><o:p></o:p></span><br />
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<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"><b><span style="color: blue;"><a href="http://www.math.iitb.ac.in/~srg/Lecnotes/afspune_des.html">Sudhir R. Ghorpade: Commutative Algebra Lecture Notes</a> >></span></b><o:p></o:p></span></div>
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<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"><i><span style="color: #660000;">1 Rings and Modules 3</span></i><o:p></o:p></span></div>
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<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"><i><span style="color: #660000;">1.1 Ideals and Radicals 3</span></i><o:p></o:p></span></div>
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<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"><i><span style="color: #660000;">1.2 Polynomial rings and Localization of rings 8</span></i><o:p></o:p></span></div>
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<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"><i><span style="color: #660000;">1.3 Modules 11</span></i><o:p></o:p></span></div>
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<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"><i><span style="color: #660000;">1.4 Zariski Topology 12</span></i><o:p></o:p></span></div>
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<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"><i><span style="color: #660000;">Exercises 14</span></i><o:p></o:p></span></div>
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<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"><i><span style="color: #660000;">2 Noetherian Rings 17</span></i><o:p></o:p></span></div>
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<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"><i><span style="color: #660000;">2.3 Artinian Rings and Modules 23</span></i><o:p></o:p></span></div>
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<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"><i><span style="color: #660000;">2.4 Krull's Principal Ideal Theorem 27</span></i><o:p></o:p></span></div>
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<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"><i><span style="color: #660000;">3.2 Noether Normalization 35</span></i><o:p></o:p></span></div>
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<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"><i><span style="color: #660000;">4 Dedekind Domains 44</span></i><o:p></o:p></span></div>
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<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"><i><span style="color: #660000;">A Appendix: Primary Decomposition of Modules 55</span></i><o:p></o:p></span></div>
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<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"><i><span style="color: #660000;">References</span></i><o:p></o:p></span><br />
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<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"><i></i><b><a href="http://ocw.mit.edu/courses/mathematics/18-705-commutative-algebra-fall-2008/" target="_blank">S. Kleiman, Commutative Algebra, MIT OpenCourseWare</a> >></b></span><br />
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<span style="color: #990000;"><span style="color: #990000;"> </span><a href="http://www.mat.uniroma3.it/users/fontana/didattica/AL410-13-14/altmankleimanCA.pdf" target="_blank"><span style="color: #990000; font-family: "arial" , "helvetica" , sans-serif;"><b>A. Altman and S. Kleiman, A Term of Commutative Algebra (2012)</b></span><span style="color: #990000;"><span style="color: #990000;"> </span><b style="font-family: arial, helvetica, sans-serif;"><span style="background-color: red; color: white;"><span style="background-color: red;">.pdf </span></span></b></span></a></span><br />
<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;"><i>Contents</i></span><br />
<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;"><i>Preface . . . . . . . . . . . . . . . . . . . . . . . iii</i></span><br />
<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;"><i>1. Rings and Ideals . . . . . . . . . . . . . . . . . . . 1</i></span><br />
<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;"><i>2. Prime Ideals . . . . . . . . . . . . . . . . . . . . 6</i></span><br />
<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;"><i>3. Radicals . . . . . . . . . . . . . . . . . . . . . . 10</i></span><br />
<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;"><i>4. Modules . . . . . . . . . . . . . . . . . . . . . . 14</i></span><br />
<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;"><i>5. Exact Sequences . . . . . . . . . . . . . . . . . . . 20</i></span><br />
<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;"><i>6. Direct Limits . . . . . . . . . . . . . . . . . . . . 26</i></span><br />
<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;"><i>7. Filtered Direct Limits . . . . . . . . . . . . . . . . . 33</i></span><br />
<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;"><i>8. Tensor Products . . . . . . . . . . . . . . . . . . . 37</i></span><br />
<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;"><i>9. Flatness . . . . . . . . . . . . . . . . . . . . . . 43</i></span><br />
<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;"><i>10. Cayley–Hamilton Theorem . . . . . . . . . . . . . . . 49</i></span><br />
<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;"><i>11. Localization of Rings . . . . . . . . . . . . . . . . . 55</i></span><br />
<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;"><i>12. Localization of Modules . . . . . . . . . . . . . . . . 61</i></span><br />
<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;"><i>13. Support . . . . . . . . . . . . . . . . . . . . . 66</i></span><br />
<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;"><i>14. Krull–Cohen–Seidenberg Theory . . . . . . . . . . . . . 71</i></span><br />
<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;"><i>15. Noether Normalization . . . . . . . . . . . . . . . . 75</i></span><br />
<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;"><i>Appendix: Jacobson Rings . . . . . . . . . . . . . . . 80</i></span><br />
<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;"><i>16. Chain Conditions . . . . . . . . . . . . . . . . . . 82</i></span><br />
<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;"><i>17. Associated Primes . . . . . . . . . . . . . . . . . . 87</i></span><br />
<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;"><i>18. Primary Decomposition . . . . . . . . . . . . . . . . 91</i></span><br />
<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;"><i>19. Length . . . . . . . . . . . . . . . . . . . . . . 97</i></span><br />
<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;"><i>20. Hilbert Functions . . . . . . . . . . . . . . . . . . 101</i></span><br />
<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;"><i>Appendix: Homogeneity . . . . . . . . . . . . . . . . 107</i></span><br />
<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;"><i>21. Dimension . . . . . . . . . . . . . . . . . . . . 109</i></span><br />
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<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;"><i>23. Discrete Valuation Rings . . . . . . . . . . . . . . . 122</i></span><br />
<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;"><i>24. Dedekind Domains . . . . . . . . . . . . . . . . . 127</i></span><br />
<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;"><i>25. Fractional Ideals . . . . . . . . . . . . . . . . . . 131</i></span><br />
<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;"><i>26. Arbitrary Valuation Rings . . . . . . . . . . . . . . . 136</i></span></div>
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<span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"><i><span style="color: #660000;">Contenuto: Teoria della dimensione; Grado di Trascendenza; Polinomi di Hilbert; Dimensione di Krull; Anelli regolari e singolari; Molteplicita. Successioni regolari ad anelli di Cohen-Macaulay; Completamenti. Metodi omologici; Introduzione agli schemi; Topologa di Zariski; Fasci di anelli e moduli; Il linguaggio dei funtori; Discesa fedelmente piatta. Morfismi étale, piatti e lisci; Differenziali algebrici; Algebre étale; Anelli Henseliani; Introduzione alle topologie di Grothendieck; La topologia étale.</span></i><o:p></o:p></span><br />
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<span style="color: #990000;"><a href="http://www.mat.uniroma3.it/users/gabelli/dispense/Campi.pdf" target="_blank"><span style="background-color: white;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-weight: bold;">S. Gabelli </span></span></span><b style="font-family: Arial, Helvetica, sans-serif;">(Università Roma Tre)</b></a><span style="background-color: white; font-family: "arial" , "helvetica" , sans-serif; font-weight: bold;"><a href="http://www.mat.uniroma3.it/users/gabelli/dispense/Campi.pdf" target="_blank">:</a> </span><span style="background-color: white; font-family: "arial" , "helvetica" , sans-serif;"> </span><a href="http://www.mat.uniroma3.it/users/gabelli/dispense/Campi.pdf" style="background-color: white; font-family: Arial, Helvetica, sans-serif;" target="_blank">Elementi di Teoria dei Campi</a></span><br />
<span style="background-color: white;"><span style="color: #990000;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="http://www.mat.uniroma3.it/users/gabelli/dispense/Campi.pdf"><br />
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<span style="color: #990000;"><a href="http://www.mat.uniroma3.it/users/gabelli/dispense/fattorizzazione.pdf" target="_blank"><span style="background-color: white;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><big><span style="font-weight: bold;"><span style="font-size: small;">S. Gabelli </span></span></big></span></span><b style="font-family: Arial, Helvetica, sans-serif;">(Università Roma Tre)</b></a></span><big style="background-color: white; font-family: Arial, Helvetica, sans-serif;"><span style="font-weight: bold;"><span style="font-size: small;"><span style="color: #990000;"><a href="http://www.mat.uniroma3.it/users/gabelli/dispense/fattorizzazione.pdf" target="_blank">:</a> </span></span></span></big><small style="background-color: white; color: #990000; font-family: Arial, Helvetica, sans-serif;"><a href="http://www.mat.uniroma3.it/users/gabelli/dispense/fattorizzazione.pdf" target="_blank"><span style="font-size: small;">Il problema della fattorizzazione nei domini di Dedekind</span></a></small></div>
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<li class="MsoNormal"><b style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #cc0000;"><a href="http://stacks.math.columbia.edu/search?keywords=commutative+ring&limit=all" target="_blank"><span style="color: #cc0000;">The Stacks Project (Columbia University) >></span></a><br /> </span></b></li>
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<b style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #990000;"><a href="http://www.math.niu.edu/~rusin/known-math/index/13-XX.html" target="_blank"><span style="color: #cc0000;">The Mathematical Atlas: Commutative rings and algebras</span><span style="color: blue;"> >></span></a></span></b></div>
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<b style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Ring_theory.html" target="_blank"><span style="color: #990000;"><span style="color: #cc0000;">The MacTutor History of Mathematics Archive: The development of ring theory</span><span style="color: blue;"> >> </span></span></a></b></div>
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<i style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #660000; mso-fareast-font-family: "Times New Roman";">The long-term goal of the Grothendieck Circle is to make publicly available (and in some cases translate) the material written by and about Alexandre Grothendieck as well as to provide biographical material on Grothendieck's life and his origins. For the present, we have posted several of his writings appearing on the web in complete form for the first time, together with many links to other online sources of his work. Since many of these texts are unpublished or are out-of-print we hope this site will serve as a valuable resource, expanding over time</span></i></div>
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<li class="MsoNormal" style="text-align: left;"><span style="color: #990000; font-family: "arial" , "helvetica" , sans-serif;"><b><a href="http://www.mat.uniroma3.it/users/fontana/didattica/documents/emmy-noether-pristem.pdf" target="_blank"><span style="color: #cc0000;">Emmy Noether. Un articolo di Aldo Brigaglia apparso su Lettera Pristem</span><span style="color: #660000;"><span style="color: #990000;"> </span><span style="background-color: red;"><span style="color: white;"> </span></span></span><span style="background-color: #f4cccc;"><span style="background-color: red; color: white;">.pdf </span></span></a><span style="color: #660000;"> </span></b><span style="color: #990000;"><o:p></o:p></span></span></li>
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<span style="color: #660000;"><span style="color: #660000; font-family: "arial";"> <b>Valutazione in itinere: Seminari, "esoneri"</b> </span><o:p></o:p></span></div>
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<span style="color: #660000;"><span style="color: maroon; font-family: "arial";">La valutazione del profitto verrà effettuata di preferenza durante il semestre. Gli studenti frequentanti saranno invitati ad effettuare almeno un seminario di approfondimento su tematiche collegate a quelle svolte a lezione.</span><o:p></o:p></span></div>
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<span style="color: #660000;"><span style="color: maroon; font-family: "arial";">Gli studenti che hanno sostenuto con esito positivo, nel corso del semestre, le prove di valutazione parziale (seminari e prove scritte) accedono direttamente al colloquio di verbalizzazione del voto proposto dal docente, da effettuarsi durante la I Sessione di esame (Appello A o B ).</span><o:p></o:p></span></div>
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<span style="color: #660000;"><span style="color: maroon; font-family: "arial";">Per tutti gli studenti che non si avvalgono della possibilità della valutazione del profitto durante il corso, l'esame finale consiste in una prova scritta (comprendente anche domande di tipo teorico) o/e orale.</span><o:p></o:p></span></div>
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<span style="color: #660000; font-family: "arial";"><span style="color: #660000;"> </span><b style="color: #660000;">Seminari </b><b style="color: #660000;"><span style="color: red;"> </span></b><span style="color: #660000;"> </span></span><span style="color: #660000;"><o:p></o:p></span></div>
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<i>[ I. Kaplansky "Commutative rings ", pp. 25-27]</i></div>
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<b><span style="color: #274e13; font-family: "arial" , "helvetica" , sans-serif;">Francesca Sardella,</span><span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"> 15 Novembre 2016: <i>Sottomoduli e moduli-quoziente. Operazioni tra moduli. Successioni esatte </i></span></b></div>
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[ M.F. Atiyah-I.G. Macdonald "Introduction to commutative algebra", pp.18-20 e 22-24]<i></i><br />
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<b><span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; mso-fareast-font-family: "Times New Roman";"><span style="color: #274e13;">Imma Marra,</span><span style="color: maroon; font-style: italic;"> 24 Novembre 2016: Il Teorema del "going-down" (GD). Approfondimento delle relazioni tra GU, INC e LO. </span></span></b></div>
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<i>[ M.F. Atiyah-I.G. Macdonald "Introduction to commutative algebra", pp. 63-64 e I. Kaplansky "Commutative rings ", pp. 28-32]<br /> </i></div>
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<b><span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"><span style="color: #274e13;">Daniele Bertotto, </span></span></b><b><span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"><b><span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; mso-fareast-font-family: "Times New Roman";"><i style="color: #660000;">1 Dicembre 2016, </i></span></b></span></b><b style="color: #660000; font-family: arial, helvetica, sans-serif;"><span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"><i>Applicazioni del BasisSatz di Hilbert: Struttura degli insiemi algebrici, varietà algebriche, irriducibilità </i></span></b></div>
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<b><span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"><i><i style="font-weight: normal;">[ D. R. Wilkins: "Topics in Commutative Algebra" (notes on-line), pp. 21-31]</i></i></span></b></div>
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<b><span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"><b><span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; mso-fareast-font-family: "Times New Roman";"><span style="color: #274e13;">Chiara Spadafora,</span><i style="color: #660000;"> <b style="color: black; font-family: Times; font-style: normal;"><span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"><b><span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; mso-fareast-font-family: "Times New Roman";"><i style="color: #660000;">6 Dicembre 2016</i></span></b></span></b>, </i></span></b><i style="color: #660000;">Condizioni sulle catene e moduli noetheriani </i></span></b></div>
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<i>[ M.F. Atiyah-I.G. Macdonald "Introduction to commutative algebra", pp. 74-78]<br /> </i></div>
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<li class="MsoNormal"><b><span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"><span style="color: #274e13;">Gaudenzio Falcone, </span></span></b><span style="color: #660000;"><b><span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"><b><span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; mso-fareast-font-family: "Times New Roman";"><i><b style="color: black; font-family: Times; font-style: normal;"><span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"><b><span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; mso-fareast-font-family: "Times New Roman";"><i style="color: #660000;">13 Dicembre 2016</i></span></b></span></b>, </i></span></b></span></b><b><span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"><i>NullstellenSatz di Hilbert: la dimostrazione di I. Kaplansky basata sui domini di Goldman</i></span></b></span><b style="color: #660000; font-family: arial, helvetica, sans-serif;"><span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif;"><i><i style="font-weight: normal;"> [ C.A. Finocchiaro MAT.632 Elective subjects - Mathematics: "Topological methods in commutative ring theory, pp. 1--8]<br /> </i></i></span></b></li>
<li class="MsoNormal"><b><span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; font-weight: normal;"><b><span style="mso-fareast-font-family: "Times New Roman";"><i>Prodotti tensoriali (complementi). Esattezza (a destra) del prodotto tensoriale. Prodotto tensoriale di algebre</i></span></b></span><span style="color: #660000; font-family: "arial" , "helvetica" , sans-serif; font-weight: normal;"><i> [ M.F. Atiyah-I.G. Macdonald "Introduction to commutative algebra", pp. 25-31]<br /> </i></span></b></li>
<li class="MsoNormal"><b>N.B.</b> Le indicazioni bibliografiche sono minimali, da integrare con altre fonti bibliografiche (sia tradizionali che on-line) indicate nella bibliografia del corso.</li>
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Unknownnoreply@blogger.comRoma, Italia41.8929163 12.48251989999994341.5147698 11.837072899999942 42.2710628 13.127966899999944