Abstract
Let M be an R-module. If every essential submodule of M has a
g-supplement in M, then M is called an essential g-supplemented (or
briefly eg-supplemented) module. If every essential submodule has ample
g-supplements in M, then M is called an amply essential g-supplemented
(or briefly amply eg-supplemented) module. In this work, some properties
of these modules are investigated. It is proved that every factor module
and every homomorphic image of an amply eg-supplemented module are amply
eg-supplemented. Let M be a projective and eg-supplemented module. Then
every finitely M-generated R-module is amply eg-supplemented.