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 **I**nstructional **C**onference on **C**ombinatorial
**T**opology and **A**lgebra, 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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