Small Pseudo Principally Quasi-Injective Acts

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Published: Oct 7, 2024
DOI: https://doi.org/10.56855/ijmme.v2i3.1124
Keywords:
Small principally quasi-injective acts, Fully small pseudo stable acts, Fully small stable acts, Small subacts

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Shaymaa Amer Abdul Kareem
Mustansiriyah University
https://orcid.org/0000-0002-5808-5890

Abstract

This work aims to present a small pseudo principally quasi-injective acts as a novel generalization of pseudo principally quasi-injective S-acts over monoids. If each S-monomorphism from a small principal subact of an S-act MS into NS can be extended to S-homomorphism from MS into NS , an S-act NS is termed as a small pseudo principally M-injective. If an S-act MS is a small pseudo principally M-injective, it is called a small pseudo principally quasi-injective. This type of generalization has several properties. Additionally, the circumstances under which subacts inherit the Small Pseudo, principally quasi-injective acts, are studied. Examples are provided to demonstrate this concept. Small pseudo principally quasi-injective acts can coincide with small principally quasi-injective acts if certain criteria are met. We discuss new characterizations of small principally quasi-injective acts. The link between classes of small, principally quasi-injective acts with other classes of injectivity is shown.

Article Details

How to Cite
Abdul Kareem, S. A. (2024). Small Pseudo Principally Quasi-Injective Acts . International Journal of Mathematics and Mathematics Education, 2(3), 139–154. https://doi.org/10.56855/ijmme.v2i3.1124
Issue
Vol. 2 No. 3 (2024)
Section
Articles

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