On a new variation of injective modules

Year 2019, Volume: 68 Issue: 1, 702 - 711, 01.02.2019

Ali Pancar Burcu Nişancı Türkmen , Celil Nebiyev , Ergül Türkmen

https://doi.org/10.31801/cfsuasmas.464103

Cited By: 2

Abstract

In this paper, we provide various properties of GE and GEE-modules, a new variation of injective modules. We call M a GE-module if it has a g-supplement in every extension N and, we call also M a GEE-module if it has ample g-supplements in every extension N. In particular, we prove that every semisimple module is a GE-module. We show that a module M is a GEE-module if and only if every submodule is a GE-module. We study the structure of GE and GEE-modules over Dedekind domains. Over Dedekind domains the class of GE-modules lies between WS-coinjective modules and Zöschinger's modules with the property (E). We also prove that, if a ring R is a local Dedekind domain, an R-module M is a GE-module if and only if M≅(R^{∗})ⁿ⊕K⊕N, where R^{∗} is the completion of R, K is injective and N is a bounded module.

Keywords

g-supplement, GE-module

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