⊕-supplemented modules as a famous generalization of lifting (projective supplemented) modules were widely studied in the last decades. In this paper, we peruse a homological approach to ⊕- supplemented modules. Let R be a ring, M a right R-module and S = EndR(M). We say that M is endomorphism ⊕-supplemented (briefly, E-⊕-supplemented) provided that for every f ∈ S, there exists a direct summand D of M such that Imf +D = M and Imf ∩D D. We investigate some general properties of E-⊕-supplemented modules and try to consider their relation with some known classes of modules such as dual Rickart modules, H-supplemented modules and ⊕-supplemented modules.
