Publication details

Pseudovarieties of Ordered Completely Regular Semigroups

Authors

ALMEIDA Jorge KLÍMA Ondřej

Year of publication 2019
Type Article in Periodical
Magazine / Source RESULTS IN MATHEMATICS
MU Faculty or unit

Faculty of Science

Citation
Web https://link.springer.com/article/10.1007/s00025-019-0998-7
Doi http://dx.doi.org/10.1007/s00025-019-0998-7
Keywords Ordered semigroup; pseudovariety; completely regular semigroup; band; complete lattice homomorphism
Description 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.
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