Pseudovarieties of completely regular semigroups

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1991 Germany English Publisher:Springer Science and Business Media LLCJournal:Semigroup Forum, volume 42, pages 1-46 (issn: 0037-1912, eissn: 1432-2137,

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Authors: Pastijn, F.;

doi: 10.1007/bf02573403

Pseudovarieties of completely regular semigroups

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Abstract

The paper explores the relationships between varieties and pseudovarieties as described by \textit{C. J. Ash} [J. Algebra 92, 104-115 (1985; Zbl 0548.08007)] to translate several main results about the lattice \(L_ v\) of varieties of completely regular semigroups into corresponding results about the lattice \(L_ p\) of pseudovarieties of finite semigroups which are completely regular. In particular, the following are obtained: (i) an analogue for \(L_ p\) of \textit{L. Polák}'s description of \(L_ v\) [Semigroup Forum 36, 253-284 (1987; Zbl 0638.20032)]; (ii) a proof that the lattice \(L_ p\) is arguesian.

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Germany

Related Organizations

Marquette University
United States
DigiZeitschriften
Germany

Keywords

Regular semigroups, Article, Varieties and pseudovarieties of semigroups, 510.mathematics, arguesian, Lattices of varieties, orthogroup, Quasivarieties, varieties of completely regular semigroups, pseudovarieties of finite semigroups, lattice

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