Goldie absolute direct summand rings and modules

Abstract

In the present paper, we introduce and study Goldie ADS modules and rings, which subsume two generalizations of Goldie extending modules due to Akalan et al. [3] and ADS-modules due to Alahmadi et al. [7]. A module M will be called a Goldie ADS module if for every decomposition M=S circle plus T of M and every complement T' of S, there exists a submodule D of M such that T'beta D and M = S circle plus D. Various properties concerning direct sums of Goldie ADS modules are established.