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Appunti on-line di corsi di introduzione all’algebra commutativa ed altri links utili
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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 [pdf file 202K].
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
1 Rings and
Modules 3
1.1 Ideals
and Radicals 3
1.2
Polynomial rings and Localization of rings 8
1.3 Modules
11
1.4 Zariski
Tolpology 12
Exercises
14
2
Noetherian Rings 17
2.1
Noetherian Rings and Modules 17
2.2 Primary
Decomposition of Ideals 19
2.3
Artinian Rings and Modules 23
2.4 Krull's
Principal Ideal Theorem 27
Exercises
14
3 Integral
Extensions 32
3.1
Integral Extensions 32
3.2 Noether
Normalization 35
3.3
Finiteness of Integral Closure 38
Exercises
42
4 Dedekind
Domains 44
4.1
Dedekind Domains 45
4.2
Extensions of Primes 50
Exercises
42
A Appendix:
Primary Decomposition of Modules 55
A.1
Associated Primes of Modules 55
A.2 Primary
Decomposition of Modules 58
Exercises
62
References
Contenuto:
Teoria della dimensione; Grado di Trascendenza; Polinomi di Hilbert; Dimensione
di Krull; Anelli regolari e singolari; Molteplicitµa. 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.
D. R. Wilkins (Trinity College, Dublin): Topics in
Commutative Algebra .pdf
A. Chambert-Loir: Algèbre commutative, Cours de master de mathématiques
.pdf
- The Mathematical Atlas: Commutative rings and algebras >>
- The MacTutor History of Mathematics Archive: The development of ring theory >>
- Grothendieck Circle >>
- 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
- Emmy Noether. Un articolo di Aldo Brigaglia apparso su Lettera Pristem .pdf
- Wolfram MathWorld: Ring theory >>
- Wikipedia: Commutative algebra >>
Le date saranno pubblicate verso fine Novembre 2012
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