Pseudovarieties of Ordered Completely Regular Semigroups

  • Jorge AlmeidaEmail author
  • Ondřej Klíma


This paper is a contribution to the theory of finite semigroups and their classification in pseudovarieties, which is motivated by its connections with computer science. The question addressed is what role is played by the consideration of an order compatible with the semigroup operation. In the case of unions of groups, so-called completely regular semigroups, the problem of which new pseudovarieties appear in the ordered context is solved. As applications, it is shown that the lattice of pseudovarieties of ordered completely regular semigroups is modular and that taking the intersection with the pseudovariety of bands defines a complete endomorphism of the lattice of all pseudovarieties of ordered semigroups.


Ordered semigroup pseudovariety completely regular semigroup band complete lattice homomorphism 

Mathematics Subject Classification

20M19 20M07 20M35 



The authors would like to thank the referees for their comments and suggestions which contributed to improve the readability of the paper.


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Authors and Affiliations

  1. 1.CMUP, Department of Matemática, Faculdade de CiênciasUniversidade do PortoPortoPortugal
  2. 2.Department of Mathematics and StatisticsMasaryk UniversityBrnoCzech Republic

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