**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

**Determinantal Rings**

by

**Winfried Bruns, Udo Vetter**-

**Springer**

Determinantal rings and varieties have been a central topic of commutative algebra and algebraic geometry. The book gives a coherent treatment of the structure of determinantal rings. The approach is via the theory of algebras with straightening law.

(

**8101**views)

**Commutative Algebra**

by

**Pete L. Clark**-

**University of Georgia**

Contents: Introduction to Commutative Rings; Introduction to Modules; Ideals; Examples of Rings; Swan's Theorem; Localization; Noetherian Rings; Boolean rings; Affine algebras and the Nullstellensatz; The spectrum; Integral extensions; etc.

(

**7616**views)

**Commutative Algebra**

by

**Jacob Lurie, Akhil Mathew**-

**Harvard University**

Topics: Unique factorization; Basic definitions; Rings of holomorphic functions; R-modules; Ideals; Localization; SpecR and Zariski topology; The ideal class group; Dedekind domains; Hom and the tensor product; Exactness; Projective modules; etc.

(

**7838**views)

**Homological Conjectures**

by

**Tom Marley, Laura Lynch**-

**University of Nebraska - Lincoln**

This course is an overview of Homological Conjectures, in particular, the Zero Divisor Conjecture, the Rigidity Conjecture, the Intersection Conjectures, Bass' Conjecture, the Superheight Conjecture, the Direct Summand Conjecture, etc.

(

**8642**views)