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. 
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     title = {Endomorphisms of {Clifford} semigroups with injective structure homomorphisms},
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     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/

[1] J. Araújo, J. Konieczny, “The Monoid of Holomorphic Endomorphisms of a Group and its Automorphisms”, Semigroups, Acts and Categories with Applications to Graphs, Estonian Mathematical Society, 2008, 7–13 | MR | Zbl

[2] Arthur H. Clifford, G. B. Preston, The algebraic theory of semigroups, v. I, Mathematical Surveys, 7, American Mathematical Society, Providence, R.I., 1961 | MR

[3] T. Gramushnjak, P. Puusemp, “A characterization of a class of $2-$groups by their endomorphism semigroups”, Generalized Lie Theory in Mathematics, Physics and Beyond, eds. Silvestrov S. et al., Springer-Verlag, Berlin, 2009, 151–159 | DOI | MR | Zbl

[4] John M. Howie, An Introduction to Semigroup Theory, Acad. Press. London, 1976 | MR | Zbl

[5] A. V. Karpenko, V. M. Misyakov, “On regularity of the center of the endomorphism ring of an abelian group”, Journal of Mathematical Sciences, 154 (2008), 304–307 | DOI | MR | Zbl

[6] J. D. P. Meldrum, “Regular semigroups of endomorphisms of groups”, Recent Developments in the Algebraic, Analytical, and Topological Theory of Semigroups, Lecture Notes in Mathematics, 998, Springer, Berlin–Heidelberg, 2006, 374–384 | DOI | MR

[7] Mario Petrich, N. Reilly, Completely Regular Semigroups, J. Wiley, New York, 1999 | MR | Zbl

[8] P. Puusemp, “Idempotents of the endomorphism semigroups of groups”, Acta et Comment. Univ. Tartuensis, 366 (1975), 76–104 (Russian) | MR | Zbl

[9] P. Puusemp, “On endomorphisms of groups of order $32$ with maximal subgroups $C_4\times C_2\times C_2$”, Proceedings of the Estonian Academy of Sciences, 63:2 (2014), 105–120 | DOI | Zbl

[10] M. Samman, J. D. P. Meldrum, “On Endomorphisms of Semilattices of Groups”, Algebra Colloquium, 12:01 (2005), 93–100 | DOI | MR | Zbl

[11] S. Worawiset, “On the endomorphism monoids of Clifford Semigroups”, Asian-European Journal of Mathematics, 11:2 (2018), 1850059, 8 pp. | DOI | MR | Zbl