More characterizations of Dedekind domains and V-rings

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.