Category:Commutative algebra
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Here is a list of articles in the Commutative algebra category of the Computing portal that unifies foundations of mathematics and computations using computers. 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.
Subcategories
This category has the following 2 subcategories, out of 2 total.
Pages in category "Commutative algebra"
The following 174 pages are in this category, out of 174 total.
- 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)