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


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.


1 Basic Constructions 2
2 Noetherian Rings 4
3 Modules 7
4 Integral Extensions 8
References 13

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