AMPLY ESSENTIAL G-SUPPLEMENTED MODULES

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 gsupplemented (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 egsupplemented.