Some Properties of R-Supplemented Modules

Abstract

In this work, r-supplemented modules are defined and some properties of these modules are investigated. It is proved that every factor module and every homomorphic image of an rsupplemented module are r-supplemented. Let M be an R-module and M = M1 +M2 +... +Mn. If Mi is r-supplemented for each i = 1, 2, ..., n, then M is also r-supplemented. Let M be an r-supplemented module. Then every finitely M-generated R-module is r-supplemented.