Category:Definitions/Algebras over Fields

This category contains definitions related to Algebras over Fields.
Related results can be found in Category:Algebras over Fields.

Let $F$ be a field.

An algebra over $F$ is an ordered pair $\struct {A, *}$ where:

$A$ is a vector space over $F$

$* : A^2 \to A$ is a bilinear mapping

That is, it is an algebra $\struct {A, *}$ over the ring $F$ where:

$F$ is a field

the $F$-module $A$ is a vector space.