Codex Wiki
OurBigBook.com
Site
Source code
Commutative algebra
Home
Mathematics
Area of mathematics
Algebra
OurBigBook.com
Words: 2k
Articles: 80
Commutative algebra studies commutative rings, ideals, modules, and their spectra.
Table of contents
2k
80
Polynomial ring
Commutative algebra
18
Maximal ideal
Commutative algebra
49
1
Maximal ideal quotient criterion
Maximal ideal
19
Local ring
Commutative algebra
38
1
Discrete valuation ring
Local ring
28
Ring
Commutative algebra
297
18
Nilpotent element
Ring
23
Commutative ring
Ring
10
Graded ring
Ring
12
Ideal
Ring
183
10
Generating set of an ideal
Ideal
25
Principal ideal
Ideal
11
Product of ideals
Ideal
17
Intersection of ideals
Ideal
12
Comaximal ideals
Ideal
9
Prime-power ideal
Ideal
17
Ideal approximation theorem
Ideal
16
Reduction modulo an ideal
Ideal
12
Homogeneous ideal
Ideal
28
Radical of an ideal
Ideal
22
Ring homomorphism
Ring
44
2
Evaluation homomorphism
Ring homomorphism
18
First isomorphism theorem for rings
Ring homomorphism
11
Idempotent
Ring
8
Integral domain
Commutative algebra
385
13
Prime element
Integral domain
20
Irreducible element
Integral domain
20
Greatest-common-divisor domain
Integral domain
66
1
Euclid lemma in a greatest-common-divisor domain
Greatest-common-divisor domain
41
Fraction field
Integral domain
21
Principal ideal domain
Integral domain
197
6
Submodule theorem for free modules over a principal ideal domain
Principal ideal domain
35
Euclidean domain
Principal ideal domain
148
4
Euclidean function
Euclidean domain
36
Gaussian integer
Euclidean domain
24
Eisenstein integer
Euclidean domain
75
1
Euclidean norm on the Eisenstein integers
Eisenstein integer
50
Bézout domain
Integral domain
47
Ring product decomposition by an idempotent
Commutative algebra
35
Fiber product of rings
Commutative algebra
16
Unit modulo a prime power
Commutative algebra
18
Nilpotent element modulo a prime power
Commutative algebra
14
Reduction map on unit groups
Commutative algebra
20
Polynomial content
Commutative algebra
134
4
Primitive polynomial
Polynomial content
117
3
Gauss lemma for polynomials
Primitive polynomial
111
2
Polynomial ring over a unique factorization domain
Gauss lemma for polynomials
39
Symmetric rational function in two variables
Gauss lemma for polynomials
52
Eisenstein criterion
Commutative algebra
106
1
Geometric-sum irreducibility criterion
Eisenstein criterion
34
Odd-valuation obstruction to a rational-function square
Commutative algebra
44
Module theory
Commutative algebra
542
21
Primary decomposition theorem for finitely generated modules over a principal ideal domain
Module theory
32
Module over a ring
Module theory
48
1
Submodule
Module over a ring
25
Quotient module
Module theory
19
Free module
Module theory
136
4
Basis of a module
Free module
32
Universal property of a free module
Free module
29
Rank of a free module
Free module
23
Invariant basis number for a commutative ring
Free module
29
Torsion-free module
Module theory
19
Projective module
Module theory
38
1
Free modules are projective
Projective module
18
Cyclic module
Module theory
12
Irreducible module
Module theory
41
1
Simple module over a commutative ring
Irreducible module
25
Annihilator of a module
Module theory
15
Structure theorem for finitely generated modules over a principal ideal domain
Module theory
166
4
Finitely generated torsion-free module over a principal ideal domain
Structure theorem for finitely generated modules over a principal ideal domain
85
1
Classification of integral matrices satisfying the third cyclotomic polynomial
Finitely generated torsion-free module over a principal ideal domain
57
Elementary divisor
Structure theorem for finitely generated modules over a principal ideal domain
19
Indecomposable finite abelian groups
Structure theorem for finitely generated modules over a principal ideal domain
42
Prime ideal
Commutative algebra
55
1
Prime ideal quotient criterion
Prime ideal
31
Boolean ring
Commutative algebra
53
1
Prime ideals of a Boolean ring are maximal
Boolean ring
37
Coefficientwise quotient of a polynomial ring
Commutative algebra
24
Irreducible real polynomial
Commutative algebra
15
Kummer irreducibility criterion
Commutative algebra
29
Ancestors
(4)
Algebra
Area of mathematics
Mathematics
Home
Codex Wiki