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  2. Category:Commutative algebra - Wikipedia
Category:Commutative algebra - Wikipedia
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From Wikipedia, the free encyclopedia

In mathematics, commutative algebra is the area of abstract algebra dealing with commutative rings and commutative modules and algebras over commutative rings. It is essential to the study of algebraic geometry and algebraic number theory.

The main article for this category is Commutative algebra.
Wikimedia Commons has media related to Commutative algebra.

Contents

  • Top
  • 0–9
  • A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Subcategories

This category has the following 3 subcategories, out of 3 total.

I

  • Invariant theory (1 C, 60 P)

L

  • Localization (mathematics) (9 P)

Σ

  • Commutative algebra stubs (61 P)

Pages in category "Commutative algebra"

The following 185 pages are in this category, out of 185 total. This list may not reflect recent changes.

 

  • Commutative algebra
  • Glossary of commutative algebra
  • List of commutative algebra topics

A

  • Abhyankar's inequality
  • Acceptable ring
  • Almost ring
  • Analytically irreducible ring
  • Analytically normal ring
  • Analytically unramified ring
  • André–Quillen cohomology
  • Arf ring
  • Artin approximation theorem
  • Artin–Rees lemma
  • Artin–Tate lemma
  • Artinian ideal
  • Ascending chain condition
  • Associated prime
  • Atomic domain
  • Auslander–Buchsbaum formula
  • Auslander–Buchsbaum theorem

B

  • Bass number
  • Bass–Quillen conjecture
  • Bézout domain
  • Buchberger's algorithm
  • Buchsbaum ring

C

  • Catenary ring
  • Change of rings
  • Chinese remainder theorem
  • Cluster algebra
  • Cohen ring
  • Cohen structure theorem
  • Cohen–Macaulay ring
  • Combinatorial commutative algebra
  • Template:Commutative local ring classes
  • Commutative ring
  • Template:Commutative ring classes
  • Complete intersection
  • Complete intersection ring
  • Completion of a ring
  • Conductor (ring theory)
  • Congruence ideal
  • Connected ring
  • Constructible topology

D

  • Dedekind domain
  • Depth (ring theory)
  • Deviation of a local ring
  • Difference of two squares
  • Differential calculus over commutative algebras
  • Differential graded algebra
  • Dimension theory (algebra)
  • Discrete valuation
  • Discrete valuation ring
  • Divided domain
  • Divided power structure
  • Dual number
  • Dualizing module

E

  • Eakin–Nagata theorem
  • Essential extension
  • Étale algebra
  • Euclidean domain
  • Excellent ring

F

  • Faltings' annihilator theorem
  • FGLM algorithm
  • Field of fractions
  • Finite algebra
  • Finitely generated algebra
  • Fitting ideal
  • Formally smooth map
  • Forster–Swan theorem

G

  • G-ring
  • GCD domain
  • Generic flatness
  • Geometrically regular ring
  • Going up and going down
  • Gorenstein ring
  • Grade (ring theory)
  • Gröbner basis
  • Gröbner fan
  • Grothendieck local duality

H

  • Hahn series
  • Hausdorff completion
  • Hensel's lemma
  • Henselian ring
  • Hilbert series and Hilbert polynomial
  • Hilbert–Burch theorem
  • Hilbert–Poincaré series
  • Hilbert–Samuel function
  • Hilbert's basis theorem
  • Hilbert's syzygy theorem
  • Hironaka decomposition
  • Hodge algebra
  • Homological conjectures in commutative algebra

I

  • I-adic topology
  • Ideal (ring theory)
  • Ideal norm
  • Ideal reduction
  • Ideal theory
  • Integer-valued polynomial
  • Integral closure of an ideal
  • Integral domain
  • Integral element
  • Integrally closed domain
  • Introduction to Commutative Algebra
  • Invariant basis number
  • Invariant polynomial
  • Invertible module
  • Irreducible ring
  • Irrelevant ideal

J

  • J-2 ring
  • J-multiplicity
  • Jacobson ring

K

  • Kähler differential
  • Koszul–Tate resolution
  • Krull dimension
  • Krull ring
  • Krull–Akizuki theorem
  • Krull's principal ideal theorem

L

  • Laurent polynomial
  • Linear equation over a ring
  • Linear relation
  • Local cohomology
  • Local criterion for flatness
  • Local parameter
  • Locally nilpotent

M

  • Matlis duality
  • Minimal prime ideal
  • Monomial conjecture
  • Mori domain
  • Mori–Nagata theorem
  • Multiplicatively closed set
  • Multiplier ideal

N

  • Nagata ring
  • Nakayama's lemma
  • Nilradical of a ring
  • Noether normalization lemma
  • Noetherian module
  • Novikov ring

O

  • Overring

P

  • Parafactorial local ring
  • Perfect ideal
  • Persistence module
  • Polynomial ring
  • Primal ideal
  • Primary decomposition
  • Primary ideal
  • Principal ideal
  • Principal ideal domain
  • Principal ideal ring
  • Prüfer domain
  • Puiseux series

Q

  • Quasi-homogeneous polynomial
  • Quasi-unmixed ring
  • Quillen–Suslin theorem

R

  • Rabinowitsch trick
  • Rees algebra
  • Rees decomposition
  • Regular ring
  • Regular sequence
  • Ring of mixed characteristic

S

  • Seminormal ring
  • Serre–Swan theorem
  • Serre's inequality on height
  • Serre's multiplicity conjectures
  • Simplicial commutative ring
  • Spectrum of a ring
  • Stanley decomposition
  • Stanley–Reisner ring
  • System of parameters

T

  • Tensor product of algebras
  • Tensor–hom adjunction
  • Test ideal
  • Tight closure
  • Top (algebra)
  • Toric ideal
  • Total ring of fractions

U

  • Unibranch local ring

V

  • Valuation ring

W

  • Wang algebra
  • Weak dimension
  • Weierstrass preparation theorem
  • Weierstrass ring
  • Wu's method of characteristic set

Z

  • Zariski ring
  • Zariski's finiteness theorem
  • Zero-divisor graph
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