Modules Whose Direct Summands Are Stable

Abstract

In this paper, we introduce and study SS-module as a proper generalization of fully stable modules. A module M is called SS-module if every direct summand of M is stable. Many characterizations and properties of SS-modules are given. For example, an R-module M is SS-module if and only if each direct summand of M fully invariant. Various known results about fully stable modules are generalized to SS-modules. For example, If M is regular SS-module, then EndR(M) is fully stable.Known modules related to SS-modules are considered. In fact, we investigate the next implications: Multiplication modules SS-modules The summand intersection property. Moreover, through examples, it can be asserted that these implications are not reversible.