Relative subcopure-injective modules

Year 2020, Volume: 69 Issue: 1, 832 - 846, 30.06.2020

Yusuf Alagöz

https://doi.org/10.31801/cfsuasmas.640331

Abstract

In this paper, copure-injective modules is examined from an alternative perspective. For two modules A and B, A is called B-subcopure-injective if for every
copure monomorphism f : B → C and homomorphism g : B → A, there exists a
homomorphism h : C → A  such that hf=g. For a module A, the
subcopure-injectivity domain of A is defined to be the collection of all
modules B such that A is B-subcopure-injective. Basic properties of the notion of subcopure-injectivity are investigated. We obtain
characterizations for various types of rings and modules, including copure-injective modules, right CDS rings and right V-rings in terms of subcopure-injectivity domains. Since
subcopure-injectivity domains clearly contains all copure-injective modules,
studying the notion of modules which are subcopure-injective only with respect
to the class of copure-injective modules is reasonable. We refer to these
modules as sc-indigent. We studied the properties of subcopure-injectivity
domains and of sc-indigent modules and investigated over some certain rings.

Keywords

Copure-injective modules, subcopure-injectivity domains, sc-indigent modules, CDS rings

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