Finitely Essential Supplemented Modules

Abstract

In this work, finitely essential supplemented modules are defined and some properties of these modules are investigated. Let M be a finitely essential supplemented module. If M is noetherian, then M is essential supplemented. Let M be a finitely essential supplemented R-module and N be a finitely generated submodule of M. Then M/N is finitely essential supplemented. Let M be a finitely essential supplemented R-module and N be a finitely generated submodule of M with RadM?N. Then M/N have no proper finitely generated essential submodules. Let M be an R-module and V?M. If V is a supplement of a finitely generated essential submodule in M, then V is called an fe-suppplement submodule in M. Let M be an R-module. If every finitely generated essential submodule of M is ?* equivalent to an fe-supplement submodule in M or M have no finitely generated essential submodules, then M is finitely essential supplemented.