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Endomorphisms of semigroups of oriented transformations

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Abstract

We characterize the monoid of endomorphisms of the semigroup of all oriented full transformations of a finite chain, as well as the monoid of endomorphisms of the semigroup of all oriented partial transformations and the monoid of endomorphisms of the semigroup of all oriented partial permutations of a finite chain. Characterizations of the monoids of endomorphisms of the subsemigroups of all orientation-preserving transformations of the three semigroups aforementioned are also given. In addition, we compute the number of endomorphisms of each of these six semigroups.

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Acknowledgements

We would like to thank the anonymous referee for his/her valuable comments and suggestions that allowed us to improve this paper. D.B. Li would like to express his gratitude to Universidade Nova de Lisboa for the hospitality during his visit.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, Gansu, People’s Republic of China

    De Biao Li

  2. Center for Mathematics and Applications (NovaMath) and Department of Mathematics, FCT NOVA, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Monte da Caparica, 2829-516, Caparica, Portugal

    Vítor H. Fernandes

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  1. De Biao Li
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  2. Vítor H. Fernandes
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Correspondence to Vítor H. Fernandes.

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Communicated by Mikhail Volkov.

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This work is partially supported by the National Natural Science Foundation of China (nos. 12271224, 12171213) and by China Scholarship Council to visit Universidade Nova de Lisboa.

This work is funded by national funds through the FCT - Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 and UIDP/00297/2020 (NovaMath - Center for Mathematics and Applications).

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Li, D.B., Fernandes, V.H. Endomorphisms of semigroups of oriented transformations. Semigroup Forum 106, 184–210 (2023). https://doi.org/10.1007/s00233-022-10325-y

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