Weakly Relative Quasi-Injective Modules

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L. S Mahmood
A. S. Mijbass
K. S. Kalaf


    Let R be a commutative ring with unity and let M, N be unitary R-modules. In this research, we give generalizations for the concepts: weakly relative injectivity, relative tightness and weakly injectivity of modules. We call M weakly N-quasi-injective, if for each f  Hom(N,ï) there exists a submodule X of ï such that  f (N) ïƒ X ≈ M, where ï is the quasi-injective hull of M. And we call M N-quasi-tight, if every quotient N / K of N which embeds in ï embeds in M. While we call M weakly quasi-injective if M is weakly N-quasiinjective for every finitely generated R-module N.         Moreover, we generalize some properties of weakly N-injective, N-tight and weakly injective modules to weakly N-quasi-injective, N-quasi-tight and weakly quasi-injective modules respectively. The relations among these concepts are also studied.

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How to Cite
Mahmood, L. S., Mijbass, A. S., & Kalaf, K. S. (2017). Weakly Relative Quasi-Injective Modules. Ibn AL- Haitham Journal For Pure and Applied Sciences, 23(1), 329–354. Retrieved from https://jih.uobaghdad.edu.iq/index.php/j/article/view/1013