An isomorphism theorem for algebras

Suppose we have given two algebras [Símbolo] and [Símbolo] over ą field F and an F- linear ∅ such that ∅ : [Símbolo] → [Símbolo] such that ∅ [Formula Matematica] and such that ∅ is a isomorphism of [Símbolo] and [Símbolo] as vector spaces over F. We wish to find necessary and sufficient condit...