# Category:Algebras

Jump to navigation
Jump to search

This category contains results about algebras over rings and fields in the context of Abstract Algebra.

Definitions specific to this category can be found in Definitions/Algebras.

Let $R$ be a commutative ring.

An **algebra over $R$** is an ordered pair $\left({A, *}\right)$ where:

- $A$ is an $R$-module
- $*: A^2 \to A$ is an $R$-bilinear mapping

## Subcategories

This category has the following 3 subcategories, out of 3 total.

### C

### D

### L

## Pages in category "Algebras"

The following 22 pages are in this category, out of 22 total.

### A

- Algebra Defined by Ring Homomorphism is Algebra
- Algebra Defined by Ring Homomorphism is Associative
- Algebra Defined by Ring Homomorphism on Commutative Ring is Commutative
- Algebra Defined by Ring Homomorphism on Ring with Unity is Unitary
- Artin's Theorem on Alternative Algebras
- Associative Algebra has Multiplicative Inverses iff Unitary Division Algebra