Endomorphisms of Clifford semigroups with injective structure homomorphisms

In the present paper, we study semigroups of endomorphisms on Clifford semigroups with injective structure homomorphisms, where the semilattice has a least element. We describe such Clifford semigroups having a regular endomorphism monoid. If the endomorphism monoid on the Clifford semigroup is comp...

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Bibliographic Details
Date:2021
Main Authors: Worawiset, S., Koppitz, J.
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2021
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Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1543
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
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Summary:In the present paper, we study semigroups of endomorphisms on Clifford semigroups with injective structure homomorphisms, where the semilattice has a least element. We describe such Clifford semigroups having a regular endomorphism monoid. If the endomorphism monoid on the Clifford semigroup is completely regular then the corresponding semilattice has at most two elements. We characterize all Clifford semigroups \(G_{\alpha}\cup G_{\beta}\) (\(\alpha >\beta \)) with an injective structure homomorphism, where \(G_{\alpha}\) has no proper subgroup, such that the endomorphism monoid is completely regular. In particular, we consider the case that the structure homomorphism is bijective.