About the course. The aim is to introduce the fundamentals of commutative algebra as applicable in other areas; notably algebraic geometry and algebraic number theory.Commutative algebra is the branch of abstract algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent examples of commutative rings include polynomial rings, rings of algebraic integers, including the ordinary integers Z, and p-adic integers

Answered by Vipan Thapar , an ibibo Master, at 7:17 PM on November 26, 2008

Commutative algebra is the branch of abstract algebra that studies commutative rings.
Commutative algebra is the main technical tool in the local study of schemes.
Hilbert introduced a more abstract approach to replace the more concrete and computationally oriented methods grounded in such things as complex analysis and classical invariant theory.
lists of commutative algebra:-
Contents [hide]
1 .Research fields
2 .Basic notions
3 .Classes of rings
4 .Constructions with commutative rings
5 .Localization and completion
6 .Finiteness properties
7 .Ideal theory
8 .Homological properties
9 .Dimension theory
10 .Ring extensions, primary decomposition
11 .Relation with algebraic geometry
12 .Computational and algorithmic aspects
13 .Active research areas
14 .Related disciplines

Answered by Ajay Kumar , an ibibo Citizen, at 7:54 PM on November 24, 2008