A semilattice of varieties of completely regular semigroups

Mario Petrich

Mathematica Bohemica (2020)

  • Volume: 145, Issue: 1, page 1-14
  • ISSN: 0862-7959

Abstract

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Completely regular semigroups are unions of their (maximal) subgroups with the unary operation within their maximal subgroups. As such they form a variety whose lattice of subvarieties is denoted by ℒ ( 𝒞 ℛ ) . We construct a 60-element ∩ -subsemilattice and a 38-element sublattice of ℒ ( 𝒞 ℛ ) . The bulk of the paper consists in establishing the necessary joins for which it uses Polák’s theorem.

How to cite

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Petrich, Mario. "A semilattice of varieties of completely regular semigroups." Mathematica Bohemica 145.1 (2020): 1-14. <http://eudml.org/doc/297320>.

@article{Petrich2020,
abstract = {Completely regular semigroups are unions of their (maximal) subgroups with the unary operation within their maximal subgroups. As such they form a variety whose lattice of subvarieties is denoted by $\mathcal \{L\}(\mathcal \{C\}\mathcal \{R\})$. We construct a 60-element $\cap $-subsemilattice and a 38-element sublattice of $\mathcal \{L\}(\mathcal \{C\}\mathcal \{R\})$. The bulk of the paper consists in establishing the necessary joins for which it uses Polák’s theorem.},
author = {Petrich, Mario},
journal = {Mathematica Bohemica},
keywords = {completely regular semigroup; lattice; variety; $\cap $-subsemilattice},
language = {eng},
number = {1},
pages = {1-14},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A semilattice of varieties of completely regular semigroups},
url = {http://eudml.org/doc/297320},
volume = {145},
year = {2020},
}

TY - JOUR
AU - Petrich, Mario
TI - A semilattice of varieties of completely regular semigroups
JO - Mathematica Bohemica
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 145
IS - 1
SP - 1
EP - 14
AB - Completely regular semigroups are unions of their (maximal) subgroups with the unary operation within their maximal subgroups. As such they form a variety whose lattice of subvarieties is denoted by $\mathcal {L}(\mathcal {C}\mathcal {R})$. We construct a 60-element $\cap $-subsemilattice and a 38-element sublattice of $\mathcal {L}(\mathcal {C}\mathcal {R})$. The bulk of the paper consists in establishing the necessary joins for which it uses Polák’s theorem.
LA - eng
KW - completely regular semigroup; lattice; variety; $\cap $-subsemilattice
UR - http://eudml.org/doc/297320
ER -

References

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