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Weakly Relative Quasi-Injective Modules | ||
| Ibn Al-Haitham Journal For Pure And Applied Science | ||
| Article 1, Volume 23, Issue 1, 2010, Pages 329-345 | ||
| Authors | ||
| K. S. Kalaf; A. S. Mijbass; L. S Mahmood | ||
| Abstract | ||
| 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, ) there exists a submodule X of such that f (N) X ≈ M, where is the quasi-injective hull of M. And we call M N-quasi-tight, if every quotient N / K of N which embeds in embeds in M. While we call M weakly quasi-injective if M is weakly N-quasi-injective 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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