More characterizations of Dedekind domains and V-rings

Authors: THUAT VAN DO, HAI DINH HOANG, SAMRUAM BAUPRADIST

Abstract: In this paper, cyclic $c-$injective modules are introduced and investigated. It is shown that a commutative Noetherian domain is Dedekind if and only if every simple module is cyclic $c-$injective. Finally, it is shown that injectivity, principal injectivity, mininjectivity, and simple injectivity are all equal to characterize right V-rings, right GV-rings, right pV-rings, and WV-rings.

Keywords: $c-$Injective modules, Dedekind domains, right V-rings, right GV-rings, WV-rings

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