# Corestriction of algebras and isomorphism

Let $L/K$ be finite and separable and $F/K$ an arbitrary extension and $E=L\otimes F$ be a field. If $A$ be $L$-algebra.

is it true that we have $F$-algebra isomorphism: $c_{L/K}(A)\otimes F\simeq c_{E/F}(A\otimes E$)?

($c_{L/K}$ is corestriction map)