Tensor product rings and Rees matrix rings. Issue 11 (19th August 2022) - Väljako, Kristo
Abstract: In this article, we study tensor product rings Q ⊗ R P, where QR and R P are R -modules for an associative ring R, and Rees matrix rings M . We will show that if S is an idempotent ring then a pseudo-surjectively defined tensor product ring Q ⊗ S P is 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.