# Category:Commutative algebra

Computing portal |

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)*