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On bases of identities of finite central locally orthodox completely regular semigroups

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Abstract

It has been known for a long time that every finite orthodox completely regular semigroup has a finite basis of identities, and that every finite central completely simple semigroup has a finite basis of identities. In the present paper, a common generalization of these two facts is established. It is shown that every finite central locally orthodox completely regular semigroup has a finite basis of identities. The proof of this latter fact which is presented in this paper employs significantly the celebrated theorem of Libor Polák on the structure of the lattice of all varieties of completely regular semigroups.

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Acknowledgements

This research has been supported by the Grant Agency of the Czech Republic under the Project GA19-12790S.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Masaryk University, Kotlářská 2, 611 37, Brno, Czech Republic

    Jiří Kad’ourek

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  1. Jiří Kad’ourek
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Correspondence to Jiří Kad’ourek.

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Communicated by Marcel Jackson.

Dedicated to the memory of Libor Polák.

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Kad’ourek, J. On bases of identities of finite central locally orthodox completely regular semigroups. Semigroup Forum 102, 697–724 (2021). https://doi.org/10.1007/s00233-021-10174-1

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