# Category:Commutative Algebra

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This category contains results about **Commutative Algebra**.

Definitions specific to this category can be found in Definitions/Commutative Algebra.

**Commutative algebra** is the branch of abstract algebra concerned with commutative and unitary rings.

## Subcategories

This category has the following 16 subcategories, out of 16 total.

### A

### C

### D

- Dedekind Domains (2 P)

### E

### F

### I

- Integral Elements (1 P)
- Integral Ring Extensions (3 P)

### L

- Local Ring Homomorphisms (1 P)

### N

- Noetherian Rings (4 P)

### P

- Primary Ideals (4 P)

### R

### T

- Transitivity of Integrality (2 P)

## Pages in category "Commutative Algebra"

The following 50 pages are in this category, out of 50 total.

### C

- Cayley-Hamilton Theorem
- Cayley-Hamilton Theorem/Finitely Generated Modules
- Characterisation of Jacobson Radical
- Chinese Remainder Theorem (Commutative Algebra)
- Chinese Remainder Theorem/Corollary
- Commutative and Unitary Ring with 2 Ideals is Field
- Contraction of Extension of Contraction of Ideal is Contraction

### E

### H

### I

- Ideal Contains Extension of Contraction
- Ideal is Contained in Contraction of Extension
- Ideal is Unit Ideal iff Includes Unity
- Ideal Quotient is Ideal
- Ideals of Field
- Injective Module over Dedekind Domain
- Injective Module over Principal Ideal Domain
- Integers form Commutative Ring with Unity
- Integral Closure is Integrally Closed
- Integral Closure is Subring
- Inverse of Division Product