A categories equivalence of associative bimodules

Abstract

In this paper we use the classical Wedderburn's Kronecker Factorization Theorem to prove that category of bimodules over $B$ and the category of bimodules over $M_{n}(B)$ are equivalent, where $B$ is some unital associative algebra. In addition to this, we classify the irreducible bimodules over $M_{n}(F).$