\begin{definition}[Definition:Linear Representation/Algebra]
Let $K$ be a field.
Let $A$ be an associative unitary algebra over $K$.
Then a '''(linear) representation of $A$''' is a vector space $V$ over $K$ equipped with a homomorphism of algebras:
:$\rho: A \to \map {\operatorname {End} } V$
where $\map {\operatorname {End} } V$ is the endomorphism ring of $V$.
Category:Definitions/Representation Theory
\end{definition}