Some Properties of Amply Weak Essential Supplemented Modules

In this work, some properties of amply weak essential supplemented modules are investigated. Let M be a projective and weakly essential supplemented module. Then every finitely M-generated module is amply weak essential supplemented. Let R be any ring. Then R is weakly essential supplemented if and only if every finitely generated R-module is amply weak essential supplemented. Let M be an amply weak essential supplemented module. Then every e-supplement submodule in M is amply weak essential supplemented.