Gamma semigroup whose gamma acts are quasi–injective

Abbas, Mehdi S.; Al-Saadi, Saad A.; Faris, Abdulqader

doi:10.47974/JDMSC-1938

Open Access Research Article

Gamma semigroup whose gamma acts are quasi–injective

^*Mehdi S. AbbasCorresponding authormsa@alzahraa.edu.iqDepartment of Mathematics College of Education Al-Zahraa University for WomenDepartment of Mathematics College of Education Al-Zahraa University for WomenKarbala, IraqView full profile → , Saad A. Al-Saadisaalsaadi@uomustansiriyah.edu.iqDepartment of Mathematics College of Science Mustansiriyah University Department of Mathematics College of Science Mustansiriyah UniversityBaghdad, 10001, Iraq0000-0002-6369-8173View full profile → , Abdulqader Farisdr.abdulkadir.faris@uoitc.edu.iqDepartment of Bioinformatics Biomedical Informatics College University of Information Technology and Communications (UOITC)Department of Bioinformatics College of Biomedical Informatics University of Information Technology and CommunicationsBaghdad, 10001, IraqView full profile →

* Corresponding author · click or hover a name for details

pp. 1561–1566Vol. 27Issue 5August 2024DOI: 10.47974/JDMSC-1938 Crossmark XML

Received:: 08 Nov 2023
Published Online:: 26 Aug 2024
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-1938
Pages:: 1561–1566

Abstract

In this paper, we interpose the notion tools, Noetherian gamma acts, and γ – idempotent elements, to describe gamma semigroups in which all gamma acts are quasi – injective. We get the following equivalent (i) a gamma semigroup S is Noetherian and each finite direct sum of quasi – injective SΓ-act is quasi – injective (ii) direct sum of quasi – injective SΓ-act is quasi – injective. Also we prove that an γ – monoid is ΓRQI if and only if all right Γ- ideal generated by γ – idempotent element.

Keywords

Gamma semigroup Gamma acts (quasi - ) injective gamma act Noetherian gamma act γ – idempotent element

Subject Classifications

Primary 20M32Secondary 08B30

References

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