The lattice of (2, 1)-congruences on a left restriction semigroup

All the (2, 1)-congruences on a left restriction semigroup become a complete sublattice of its lattice of congruences. The aim of this article is to study certain fundamental properties of this complete sublattice. We introduce -, -, -, and -operators on this sublattice and obtain some properties. A...

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Bibliographic Details
Published inOpen mathematics (Warsaw, Poland) Vol. 20; no. 1; pp. 1159 - 1172
Main Authors Liu, Haijun, Guo, Xiaojiang
Format Journal Article
LanguageEnglish
Published Warsaw De Gruyter 12.10.2022
De Gruyter Poland
Subjects
(2, 1)-congruences
20M10
20M75
complete lattices
Congruences
Lattices (mathematics)
left restriction semigroups
projection kernel-traces
Semigroups
semilattices
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Summary:All the (2, 1)-congruences on a left restriction semigroup become a complete sublattice of its lattice of congruences. The aim of this article is to study certain fundamental properties of this complete sublattice. We introduce -, -, -, and -operators on this sublattice and obtain some properties. As applications, the remarkable (2, 1)-congruences are characterized. These results extend the corresponding results on inverse semigroups and ample semigroups.
ISSN:2391-5455
2391-5455
DOI:10.1515/math-2022-0492