Simple-Direct Modules Over Formal Matrix Rings

Abstract

Abstract: In the present paper, we study simple-direct-injective modules and simple-direct-projective modules over a formal matrix ring (Formula presented.), where M is an (R,S)-bimodule and N is a (S,R)-bimodule over rings R and S. We determine necessary and sufficient conditions for a K-module to be, respectively, simple-direct-injective or simple-direct-projective. We also give some examples to illustrate and delimit our results.