Symmetric modules over their endomorphism rings

Abstract

Let R be an arbitrary ring with identity and M a right R-module with S=EndR(M). In this paper, we study right R-modules M having the property for f,g∈EndR(M) and for m∈M, the condition fgm=0 implies gfm=0. We prove that some results of symmetric rings can be extended to symmetric modules for this general setting.