Relative subcopure-injective modules
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Date
2020-06-30
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Ankara Üniversitesi Fen Fakültesi
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.
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Copure-injective modules, Subcopure-injectivity domains, Sc-indigent modules