Congruence-injective acts over monoid

Faris, Abdulqader; Aziz, Mustafa A.; Al-Saadi, Saad A.

doi:10.47974/JDMSC-2717

Open Access Research Article

Congruence-injective acts over monoid

^*Abdulqader FarisCorresponding authordr.abdulkadir.faris@uoitc.edu.iqDepartment of BioinformaticsCollege of Biomedical InformaticsUniversity of Information Technology and CommunicationsBaghdad, IraqView full profile → , Mustafa A. Azizmustafa.a.aziz@uomustansiriyah.edu.iqDepartment of MathematicsCollege of ScienceMustansiriyah UniversityBaghdad, IraqView full profile → , Saad A. Al-Saadisaalsaadi@uomustansiriyah.edu.iqDepartment of MathematicsCollege of ScienceMustansiriyah UniversityBaghdad, Iraq0000-0002-6369-8173View full profile →

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pp. 2147–2152Vol. 29Issue 5May 2026DOI: 10.47974/JDMSC-2717 Crossmark XML

Received:: 01 Jan 2026
Published Online:: 22 May 2026
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-2717
Pages:: 2147–2152

Abstract

This article introduces and studies the concept of congruence-injective S-act over monoids S as a new generalization of injectivity in act theory. This approach is based on congruence and extends the notions of quasi-injective and pseudo-injective S-acts. The main outcome of this study is a characterization theorem for congruence-injective S-acts with respect to perfect congruence. From this result, we obtain a new characterization of quasi-injective acts, which parallels in L. Fuchs’s classical result for module theory. These contributions enrich the theory of injectivity in the category of acts.

Keywords

Monoid S-acts Injective acts Quasi-injective acts Congruence Regular gamma semigroups

Subject Classifications

Primary 93A30Secondary 49K15

References

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