Definition:Linear Representation/Algebra

Definition
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:


 * $\rho: A \to \operatorname{End} \left({V}\right)$

where $\operatorname{End}\left({V}\right)$ is the endomorphism ring of $V$.