Turkish Journal of Mathematics
DOI
-
Abstract
Let R be a commutative ring with identity and M be an R-module with Spec(M) \neq \phi. A cover of the R-submodule K of M is a subset C of Spec(M) satisfying that for any x \in K, x \neq 0, there is N \in C such that ann(x) \subset (N:M). If we denote by J = \bigcap_{N \in C} (N:M) and assume that M is finitely generated, then JM=M implies that M=0, M is called C-injective provided each R-homomorphism \phi : (N:M) \rightarrow M with N \in C can be lifted to an R-homomorphism \lambda : R \rightarrow M. If R is a commutative Noetherian ring and C'=Spec(R), where C'={(N:M) N \in C}, then every C-injective R-module is injective.
Keywords
Commutative ring, D-prime module cover, prime submodule, injective module, quasi-injective and injective hull
First Page
111
Last Page
116
Recommended Citation
AMIRI, N. (2008) "Cover for Modules and Injective Modules," Turkish Journal of Mathematics: Vol. 32: No. 1, Article 10. Available at: https://journals.tubitak.gov.tr/math/vol32/iss1/10
