Some Concepts Related to Almost Injective(Projective)Semi modules

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Khitam Sahib Aljebory
Assad Mohammed Alhossaini

Abstract

         In this research,  the concepts injective and projective semi modules have been generalized to generalized-injective(projective) and essentially-injective semimodules, also the relationship of these concepts with  almost-injective(projective) semimodules have been discussed. The semiring having the properties that every quasi- injective semimodule is injective and every almost self-injective semimodule is injective have been defined. Some results between these concepts  have been obtained like, every almost-injective is generalized-injective semimodule,  the definitions, where a semi module is indecomposable have been discussed.  Dually for almost-projective semimodule. Also obtained that, the direct sum of two quasi-injective Ȑ-semimodule is quasi-injective when  Ȑ is QI-semiring, this fact has been expanded to AQI-semiring.


Conclusion: In this paper, several generalization of injective and projective semi modules  have been defined and some concepts with related to almost injective(projective)semimodules have been presented, also  the concepts QI-semiring, AQI-semiring defined, some relationship between these concepts and almost injective(projective) semimodules discussed.

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How to Cite
[1]
“Some Concepts Related to Almost Injective(Projective)Semi modules”, JUBPAS, vol. 31, no. 1, pp. 111–121, Apr. 2023, doi: 10.29196/jubpas.v31i1.4533.
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How to Cite

[1]
“Some Concepts Related to Almost Injective(Projective)Semi modules”, JUBPAS, vol. 31, no. 1, pp. 111–121, Apr. 2023, doi: 10.29196/jubpas.v31i1.4533.

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