Geodesic
Endomorphisms of Clifford semigroups with injective structure homomorphisms
Algebra and discrete mathematics, Tome 30 (2020) no. 2, pp. 290-304

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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.
Keywords: Clifford semigroups, endomorphism monoid, regular. 
@article{ADM_2020_30_2_a12,
     author = {S. Worawiset and J. Koppitz},
     title = {Endomorphisms of {Clifford} semigroups with injective structure homomorphisms},
     journal = {Algebra and discrete mathematics},
     pages = {290--304},
     publisher = {mathdoc},
     volume = {30},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2020_30_2_a12/}
}
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S. Worawiset; J. Koppitz. Endomorphisms of Clifford semigroups with injective structure homomorphisms. Algebra and discrete mathematics, Tome 30 (2020) no. 2, pp. 290-304. http://geodesic.mathdoc.fr/item/ADM_2020_30_2_a12/