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 5 subcategories, out of 5 total.
Pages in category "Algebras"
The following 23 pages are in this category, out of 23 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