List of commutative algebra topics

Summary

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 , and p-adic integers.

Research fields edit

Active research areas edit

Basic notions edit

Classes of rings edit

Constructions with commutative rings edit

Localization and completion edit

Finiteness properties edit

Ideal theory edit

Homological properties edit

Dimension theory edit

Ring extensions, primary decomposition edit

Relation with algebraic geometry edit

Computational and algorithmic aspects edit

Active research areas edit

Related disciplines edit