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Journals / Hacettepe Journal of Mathematics and Statistics / 2017 / Volume: 46 Issue: 6

A structure theorem of left regular cyber-groups

Ying Yuan
Xueming Ren
K. P. Shum
Pages
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Publication Date
2017-12-01
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

After the investigation of the properties of superabundant semigroups, we establish a structure theorem for the left regular cybergroups by using the newly defined left twist product of semigroups.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:An abundant semigroup S is a superabundant semigroup if each $\mathcal{H}^*$-class of S contains an idempotent.
📊
Key Findings & Data:We call a superabundant semigroup a left regular cyber-group if the set of its idempotents forms a left regular band.
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Conclusion & Impact:After the investigation of the properties of superabundant semigroups, we establish a structure theorem for the left regular cybergroups by using the newly defined left twist product of semigroups.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Completely regular semigroups · Superabundant semigroups · Left regular cyber-groups

Abstract

An abundant semigroup S is a superabundant semigroup if each $\mathcal{H}^*$-class of S contains an idempotent. We call a superabundant semigroup a left regular cyber-group if the set of its idempotents forms a left regular band. After the investigation of the properties of superabundant semigroups, we establish a structure theorem for the left regular cybergroups by using the newly defined left twist product of semigroups.

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Cite This Article

Yuan, Y., Ren, X., Shum, K. P. (2017). A structure theorem of left regular cyber-groups. Hacettepe Journal of Mathematics and Statistics, Volume: 46 Issue: 6. https://ajindex.com/articles/1402989

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