Some Concepts Related to Almost Injective(Projective)Semi modules

Khitam Sahib Aljebory; Assad Mohammed Alhossaini

doi:10.29196/jubpas.v31i1.4533

Article Details

Some Concepts Related to Almost Injective(Projective)Semi modules

Authors:

Khitam Sahib Aljebory | Assad Mohammed Alhossaini

Publisher:

University of Babylon

Journal:

JOURNAL OF UNIVERSITY OF BABYLON for Pure and Applied Sciences Vol.31 Issue 1, pp.111-121

Document Type:

Article

Publication Date:

3/2023

Document Language:

English

Document ID (Org No.):

2001383143

pISSN:

2312-8135

DOI:

10.29196/jubpas.v31i1.4533

Keywords:

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.

Article Details

Some Concepts Related to Almost Injective(Projective)Semi modules

Authors:

Khitam Sahib Aljebory | Assad Mohammed Alhossaini

Publisher:

University of Babylon

Journal:

JOURNAL OF UNIVERSITY OF BABYLON for Pure and Applied Sciences Vol.31 Issue 1, pp.111-121

Document Type:

Article

Publication Date:

3/2023

Document Language:

English

Document ID (Org No.):

2001383143

pISSN:

2312-8135

DOI:

10.29196/jubpas.v31i1.4533

Semimodules

Semirings

Issues

Article Details

Some Concepts Related to Almost Injective(Projective)Semi modules

Authors: Khitam Sahib Aljebory | Assad Mohammed Alhossaini

Publisher: University of Babylon

Journal: JOURNAL OF UNIVERSITY OF BABYLON for Pure and Applied Sciences Vol.31 Issue 1, pp.111-121

Document Type: Article

Publication Date: 3/2023

Document Language: English

Document ID (Org No.): 2001383143

pISSN: 2312-8135

DOI: 10.29196/jubpas.v31i1.4533

Semimodules

Semirings

Issues

Authors:

Khitam Sahib Aljebory | Assad Mohammed Alhossaini

Publisher:

University of Babylon

Journal:

JOURNAL OF UNIVERSITY OF BABYLON for Pure and Applied Sciences Vol.31 Issue 1, pp.111-121

Document Type:

Article

Publication Date:

3/2023

Document Language:

English

Document ID (Org No.):

2001383143

pISSN:

2312-8135

DOI:

10.29196/jubpas.v31i1.4533