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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