Tensor product rings and Rees matrix rings. Issue 11 (19th August 2022)

• Record Type: Journal Article
• Authors: Väljako, Kristo
• Is Part Of: Communications in algebra. Volume 50:Issue 11(2022)
• Page Start: 4945
• Page End: 4963
• Publication Date: 2022-08-19
• Subjects: Morita context -- Morita equivalence -- Rees matrix ring -- Ring -- tensor product ring; 16D90; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2022.2078342
• Languages: English
• ISSNs: 0092-7872

Abstract

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.