Goldie ss-supplemented modules

Abstract

In this study, it has been determined the notion of Goldie ss-supplemented modules by the help of the relation (Formula Presented), which is defined in the form (Formula Presented), which provides conditions both of (Formula Presented) and (Formula Presented) for submodules W and Z of module A is an equivalence relation. The main features of Goldie ss-supplemented modules provided by this relation is examined. It is shown that the epimorphism (Formula Presented) provided the relation (Formula Presented) under certain conditions and the relation (Formula Presented), is expressed in the maximal submodules. In addition, we obtain notions of Goldie ss-lifting modules using the relation (Formula Presented) and we prove several properties of notions of these modules. © 2023, MTJPAM Turkey. All rights reserved.