N. AMIRI

Cover for Modules and Injective Modules

Let R be a commutative ring with identity and M be an R-module with Spec(M) \neq f. 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 = \bigcapN \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 f : (N:M) \rightarrow M with N \in C can be lifted to an R-homomorphism l : 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.

Anahtar Kelimeler:

Commutative ring, D-prime module cover, prime submodule, injective module, quasi-injective and injective hull

Cover for Modules and Injective Modules

Keywords:

Commutative ring, D-prime module cover, prime submodule, injective module, quasi-injective and injective hull,

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Amiri, N., Ershad, M. and Sharif, H.: Cover for Modules, To appear in International Journal Of Commutative Ring. Anderson, F. W. and Fuller, K. P.: Ring and Categories of Modules Springer-Verlag (1974).
Gooderl, K. R.: Von Neumann Regular Ring, Pitman, 1979.
Matsumura, H.: Commutative ring theory, Cambridge university Press, 1986. N. AMIRI
Department of Mathematics, Payame Nour University of Firouzabad, Firouzabad, 71454, IRAN e-mail: amiri@susc.ac.ir