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. © Journal “Algebra and Discrete Mathematics”.