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Commutative algebra

Table of contents

Localization (mathematics)

Hasse principle

Local analysis

Local ring

Semi-local ring

Acceptable ring

Almost ring

Analytically irreducible ring

Analytically normal ring

Analytically unramified ring

Arf ring

Artin approximation theorem

Artinian ideal

Ascending chain condition

Atomic domain

Auslander–Buchsbaum formula

Auslander–Buchsbaum theorem

Bass number

Bass–Quillen conjecture

Buchsbaum ring

Bézout domain

Catenary ring

Change of rings

Cluster algebra

Cohen ring

Cohen structure theorem

Cohen–Macaulay ring

Complete intersection

Complete intersection ring

Completion of a ring

Conductor (ring theory)

Congruence ideal

Connected ring

Constructible topology

Deviation of a local ring

Differential calculus over commutative algebras

Differential graded algebra

Discrete valuation ring

Divided domain

Dualizing module

Eakin–Nagata theorem

Euclidean domain

Excellent ring

Finite algebra

Finitely generated algebra

Fitting ideal

Formally smooth map

G-ring

GCD domain

Geometrically regular ring

Glossary of commutative algebra

Going up and going down

Gorenstein ring

Hahn series

Hausdorff completion

Henselian ring

Hilbert's basis theorem

Hilbert's syzygy theorem

Hilbert series and Hilbert polynomial

Hilbert–Samuel function

Hironaka decomposition

Hodge algebra

Homological conjectures in commutative algebra

I-adic topology

Ideal norm

Ideal reduction

Ideal theory

Integral domain

Integrally closed domain

Introduction to Commutative Algebra

Irreducible ring

Irrelevant ideal

J-2 ring

J-multiplicity

Jacobson ring

Koszul–Tate resolution

Krull's principal ideal theorem

Krull ring

List of commutative algebra topics

Local criterion for flatness

Local parameter

Locally nilpotent

Minimal prime ideal

Monomial conjecture

Mori domain

Mori–Nagata theorem

Multiplicatively closed set

Multiplier ideal

Nagata ring

Nilradical of a ring

Novikov ring

Parafactorial local ring

Perfect ideal

Primal ideal

Primary decomposition

Primary ideal

Principal ideal

Principal ideal domain

Principal ideal ring

Prüfer domain

 Ancestors (4)

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