Category:Commutative algebra

• Commutative algebra (computing)
• Glossary of commutative algebra (computing)
• List of commutative algebra topics (computing)

A

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

B

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

C

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

D

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

E

• Eakin–Nagata theorem (computing)
• Essential extension (computing)
• Étale algebra (computing)
• Euclidean domain (computing)
• Excellent ring (computing)
• Extension and contraction of ideals (computing)

F

• FGLM algorithm (computing)
• Field of fractions (computing)
• Finite algebra (computing)
• Finitely generated algebra (computing)
• Fitting ideal (computing)
• Formally smooth map (computing)

G

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

H

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

I

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

J

• J-2 ring (computing)
• J-multiplicity (computing)
• Jacobson ring (computing)

K

• Kähler differential (computing)
• Koszul–Tate resolution (computing)
• Krull dimension (computing)
• Krull ring (computing)
• Krull's principal ideal theorem (computing)

L

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

M

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

N

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

P

• Parafactorial local ring (computing)
• Polynomial ring (computing)
• Primal ideal (computing)
• Primary decomposition (computing)
• Primary ideal (computing)
• Principal ideal (computing)
• Principal ideal domain (computing)
• Principal ideal ring (computing)
• Prüfer domain (computing)
• Puiseux series (computing)

Q

• Quasi-homogeneous polynomial (computing)
• Quasi-unmixed ring (computing)
• Quillen–Suslin theorem (computing)

R

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

S

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

T

• Tensor product of algebras (computing)
• Tensor-hom adjunction (computing)
• Test ideal (computing)
• Tight closure (computing)
• Top (mathematics) (computing)
• Total ring of fractions (computing)

U

• Unibranch local ring (computing)

V

• Valuation ring (computing)

W

• Weak dimension (computing)
• Weierstrass preparation theorem (computing)
• Weierstrass ring (computing)
• Wu's method of characteristic set (computing)

Z

• Zariski ring (computing)
• Zariski's finiteness theorem (computing)
• Zero-divisor graph (computing)