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All Journal International Journal of Mathematics and Mathematics Education (IJMME)
Abdul Kareem, Shaymaa Amer
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Mathematics

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Small Pseudo Principally Quasi-Injective Acts Abdul Kareem, Shaymaa Amer
International Journal of Mathematics and Mathematics Education (IJMME) Vol. 2 No. 3 (2024)
Publisher : EDUPEDIA Publisher

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.56855/ijmme.v2i3.1124

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.
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