Tensor product rings and Rees matrix rings

Abstract

In this article, we study tensor product rings $Q{\otimes }_{R}P,$ where Q_R and ${}_{R}P$ are R-modules for an associative ring R, and Rees matrix rings $\mathcal{M}.$ We will show that if S is an idempotent ring then a pseudo-surjectively defined tensor product ring $Q{\otimes }_{S}P$ 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.

Keywords:

• Morita context
• Morita equivalence
• Rees matrix ring
• Ring
• tensor product ring

2020 Mathematics Subject Classification:

• 16D90

Acknowledgement

I would like to express my gratitude to professor Valdis Laan and professor Mart Abel for several useful comments and suggestions.

Additional information

Funding

Research was supported by the University of Tartu ASTRA Project PER ASPERA, financed by the European Regional Development Fund, and by the Estonian Research Council grant PRG1204.