- Turkish Journal of Mathematics
- Vol: 41 Issue: 1
- More characterizations of Dedekind domains and V-rings
More characterizations of Dedekind domains and V-rings
Authors : Thuat Van Do, Hai Dinh Hoang, Samruam Baupradist
Pages : 33-42
View : 6 | Download : 4
Publication Date : 9999-12-31
Article Type : Makaleler
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