A Quick Review of Commutative Algebra
A Quick Review of Commutative Algebra
Sudhir R. Ghorpade
Department of Mathematics
Indian Institute of Technology, Bombay
Powai, Mumbai 400076 India
E-mail: srg@math.iitb.ac.in
Version 1.2, February 2000
Description
These notes are a slightly revised and expanded version of the first chapter
of the Lecture Notes of the NBHM
sponsored Instructional Conference on Combinatorial
Topology and Algebra, held at
IIT Bombay in December 1993. They
attempt to give a rapid review of the rudiments of classical
commutative algebra. Some of the main results whose proofs are outlined here
are: Hilbert basis theorem, primary decomposition of ideals in
noetherian rings, Krull intersection theorem, Going up and Going down theorems
for integral extensions, Noether's Normalization Lemma and
Hilbert's Nullstellensatz.
Contents
| 1 | Basic Constructions | 2 |
| 2 | Noetherian Rings | 4 |
| 3 | Modules | 7 |
| 4 | Integral Extensions | 8 |
| | References | 13 |
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