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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
We consider many relationships between weakly regular S-acts and locally projective S-acts.
📌 3 Key Takeaways
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Objective & Hypothesis:We generalize the concept of weakly regularity in semigroups to S-acts, where S is a monoid.
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Key Findings & Data:We prove among other results that if a monoid is von-Neumann regular then weakly regularity and von-Neumann regularity, in the context of S-acts, coincide.
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Conclusion & Impact:We consider many relationships between weakly regular S-acts and locally projective S-acts.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:S-acts · Monoids · Projective S-acts
Abstract
We generalize the concept of weakly regularity in semigroups to S-acts, where S is a monoid. We prove among other results that if a monoid is von-Neumann regular then weakly regularity and von-Neumann regularity, in the context of S-acts, coincide. We also define locally projective S-acts, which is the generalization of projective S-acts. We consider many relationships between weakly regular S-acts and locally projective S-acts.
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Cite This Article
SHABİR, M., KHALİQ, I., IMRAN, G. (2022). Characterization of Weakly Regular S-acts. Hacettepe Journal of Mathematics and Statistics, Cilt: 43 - Sayı: 5, 753–761. https://ajindex.com/articles/530314