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Pseudo-Weakly-N-Quasi- Injective Modules | ||
| Tikrit Journal of Pure Science | ||
| Article 1, Volume 13, Issue 2, 2008, Pages 70-75 | ||
| Author | ||
| Haibat K. Mohammadali | ||
| Abstract | ||
| Let R be a commutative ring with unity and M be a unitary R-module. An R-module M is said to be N-injective where N is an R-module if for each , where E(M) is the injective hull of M. And M is called weakly-N-injective if for each there exists a submodule X of E(M) such that . In this paper we give generalizations for the concepts N-injective and weakly- N-injective modules we call them pseudo-N-quasi-injective and pseudo-weakly-N-quasi-injective modules respectively. We call an R-module M pseudo-N-quasi-injective modules if for each monomorphism where is quasi injective hull of M. And we call M is Pseudo-weakly-N-quasi-injective module if for each monomorphism , there exists a submodule X of such that . Our main goal in this work is to study the basic properties of these concepts, and give examples, characterizations of pseudo-weakly-N-quasi-injective and study the relation of these concepts with other modules. | ||
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