A conjecture for varieties of completely regular semigroups-Reference-Cited by-同舟云学术

A conjecture for varieties of completely regular semigroups

Published:2019-05-21 Issue:3 Volume:69 Page:541-556
ISSN:1337-2211
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Petrich Mario¹

Affiliation:

1. , 21420 Bol , Brač , Croatia

Abstract

Abstract The class 𝒞ℛ of completely regular semigroups considered with the unary operation of inversion within maximal subgroups forms a variety. The B-relation on the lattice ℒ(𝒞ℛ) of subvarieties of 𝒞ℛ identifies two varieties if they contain the same bands. Its classes are intervals with the set Δ of upper ends of these intervals. Canonical varieties form part of Δ. Previously we determined the sublattice Ψ of ℒ(𝒞ℛ) generated by the variety 𝒞𝒮 of completely simple semigroups and six canonical varieties. The conjecture is that the sublattice of ℒ(𝒞ℛ) generated by 𝒞𝒮 and canonical varieties follows the pattern of the structure of Ψ.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2017-0246/pdf

Reference12 articles.

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5. Petrich, M.: Canonical varieties of completely regular semigroups, J. Aust. Math. Soc. 83 (2007), 87–104.

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