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In this article, we study tensor product ringswhere  Q Randare  R -modules for an associative ring  R , and Rees matrix ringsWe will show that if  S  is an idempotent ring then a pseudo-surjectively defined tensor product ringis Morita equivalent to  S  and that an idempotent Rees matrix ring is Morita equivalent to its ground ring  R . We will prove that for an idempotent Rees matrix ring there exists a strictly locally isomorphic tensor product ring. It is shown that, under some assumptions, a tensor product ring is isomorphic to a certain subring of the ring of adjoint endomorphisms.

Tensor product rings and Rees matrix rings