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On Some Injective Modules In σ[M]

A. Çiğdem Özcan, Derya Keskı̇n Tütüncü, Mohamed Yousif

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Abstract

In this paper, we study the notions (strongly) soc-injective, (strongly) simple-injective and (strongly) mininjective modules in σ[M]. For any module N in σ[M], N is strongly mininjective in σ[M] if and only if it is strongly simple-injective in σ[M]. A module M is locally Noetherian if and only if every strongly simple-injective module in σ[M] is strongly soc-injective. We also characterize Noetherian QF-modules.

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What this paper is about

In this paper, we study the notions (strongly) soc-injective, (strongly) simple-injective and (strongly) mininjective modules in σ[M]. For any module N in σ[M], N is strongly mininjective in σ[M] if and only if it is strongly simple-injective in σ[M]. A module M is locally Noetherian if and only if every strongly simple-injective module in σ[M] is strongly soc-injective. We also characterize Noetherian QF-modules.

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Available abstract

In this paper, we study the notions (strongly) soc-injective, (strongly) simple-injective and (strongly) mininjective modules in σ[M]. For any module N in σ[M], N is strongly mininjective in σ[M] if and only if it is strongly simple-injective in σ[M]. A module M is locally Noetherian if and only if every strongly simple-injective module in σ[M] is strongly soc-injective. We also characterize Noetherian QF-modules.

Key concepts: Injective function, Injective module, Noetherian, Simple (philosophy), Mathematics, Simple module, Pure mathematics, Horizontal line test

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