On a New Variation of Injective Modules

Abstract

In this paper, we provide various properties of GE and GEEmodules, a new variation of injective modules. We call M a GE-module if ithas a g-supplement in every extension N and, we call also M a GEE-moduleif it has ample g-supplements in every extension N. In particular, we provethat every semisimple module is a GE-module. We show that a module M isa GEE-module if and only if every submodule is a GE-module. We study thestructure of GE and GEE-modules over Dedekind domains. Over Dedekinddomains the class of GE-modules lies between W S-coinjective modules andZˆschingerís modules with the property (E). We also prove that, if a ring Ris a local Dedekind domain, an R-module M is a GE-module if and only ifM = (R)n K N, where R is the completion of R, K is injective and Nis a bounded module.