List of commutative algebra topics
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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): \mathbb {Z} , and p-adic integers.
Research fields
Active research areas
Basic notions
Classes of rings
Constructions with commutative rings
Localization and completion
Finiteness properties
Homological properties
Dimension theory
Ring extensions, primary decomposition
Relation with algebraic geometry
Computational and algorithmic aspects
Active research areas
Related disciplines
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