**A Quick Review of Commutative Algebra**

by Sudhir R. Ghorpade

**Publisher**: Indian Institute of Technology, Bombay 2000**Number of pages**: 13

**Description**:

These notes 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.

Download or read it online for free here:

**Download link**

(200KB, PDF)

## Similar books

**Theory and Applications of Lattice Point Methods for Binomial Ideals**

by

**Ezra Miller**-

**arXiv**

This is a survey of lattice point methods for binomial ideals. It is aimed at students and researchers in algebra; it includes many examples, open problems, and elementary introductions to the motivations and background from outside of algebra.

(

**9135**views)

**Commutative Algebra**

by

**Keerthi Madapusi**-

**Harvard University**

Contents: Graded Rings and Modules; Flatness; Integrality: the Cohen-Seidenberg Theorems; Completions and Hensel's Lemma; Dimension Theory; Invertible Modules and Divisors; Noether Normalization and its Consequences; Quasi-finite Algebras; etc.

(

**11449**views)

**The CRing Project: a collaborative open source textbook on commutative algebra**

by

**Shishir Agrawal, et al.**-

**CRing Project**

The CRing project is an open source textbook on commutative algebra, aiming to comprehensively cover the foundations needed for algebraic geometry at the EGA or SGA level. Suitable for a beginning undergraduate with a background in abstract algebra.

(

**9963**views)

**Frobenius Splitting in Commutative Algebra**

by

**Karen E. Smith, Wenliang Zhang**-

**arXiv**

Frobenius splitting has inspired a vast arsenal of techniques in commutative algebra, algebraic geometry, and representation theory. The purpose of these lectures is to give a gentle introduction to Frobenius splitting for beginners.

(

**7157**views)