Separable algebra (reviewed)

A (finite) separable algebra $A$ over a field $F$, also called an étale $F$-algebra, is an $F$-algebra of finite dimension that is isomorphic to a product of separable field extensions of $F$.

If $L/K$ is a field extension and $A$ is a separable $K$-algebra then $A\otimes_K L$ is a separable $L$-algebra (which is typically not a field, even when $A$ is).