A new approach to H -supplemented modules via homomorphisms

Abstract

The class of H -supplemented modules, which is a nice generalization of that of lifting modules, has beenstudied extensively in the last decade. As the concept of homomorphisms plays an important role in module theory, weare interested in H -supplemented modules relative to homomorphisms. Let R be a ring, M a right R-module, and S =End R(M). We say that M is endomorphism H -supplemented (briefly, E -H -supplemented) provided that for everyf ∈ S there exists a direct summand D of M such that Imf + X = M if and only if D + X = M for every submoduleX of M . In this paper, we deal with the E -H -supplemented property of modules and also a similar property for amodule M by considering Hom R(N, M) instead of S where N is any module.