From Wikipedia, the free encyclopedia
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
Active research areas
Basic notions
Classes of rings
Constructions with commutative rings
Localization and completion
Finiteness properties
Ideal theory
Homological properties
Dimension theory
Ring extensions, primary decomposition
Relation with algebraic geometry
Computational and algorithmic aspects
Active research areas
Related disciplines