# Category:Algebras

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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 $\struct {A, *}$ where:

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

## Subcategories

This category has the following 30 subcategories, out of 30 total.

### *

### A

- Algebra Homomorphisms (empty)
- Alternative Algebras (3 P)
- Associators (1 P)

### C

- Cayley-Dickson Construction (6 P)
- Conjugations on Algebras (empty)

### D

### E

- Examples of Algebras (empty)

### F

### G

### I

### L

- Lie Algebras (3 P)

### M

### N

- Non-Associative Algebras (1 P)

### P

- Pointed Algebras (empty)
- Power-Associative Algebras (empty)

### Q

- Quadratic Real Algebras (empty)

### R

- Real Algebras (empty)

### S

### U

## Pages in category "Algebras"

The following 16 pages are in this category, out of 16 total.