Identities and isomorphisms of finite-dimensional graded simple algebras

Abstract

Let $\mathbb{F}$ be an algebraically closed field, $G$ be an abelian group, and let $A$ and $B$ be arbitrary finite-dimensional $G$-graded simple algebras over $\mathbb{F}$. We prove that $A$ and $B$ are isomorphic if, and only if, they satisfy the same graded polynomial identities.

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