Essential Radical Supplemented Modules

Abstract

In this work, (amply) essential radical supplemented modules are defined and some properties of these modules are investigated. Let M be an R-module and M = M-1 + M-2 + ... + M-n. If M-i is essential radical supplemented for every i = 1, 2, ..., n, then M is also essential radical supplemented. It is proved that every factor module and every homomorphic image of an essential radical supplemented module are essential radical supplemented. Let M be an essential radical supplemented R-module. Then every finitely M-generated R-module is essential radical supplemented.