Abstract

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 k-, K-, t-, and T-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.

Details

Title
The lattice of (2, 1)-congruences on a left restriction semigroup
Author
Liu, Haijun 1 ; Guo, Xiaojiang 2 

1  School of Mathematics and Statistics, Jiangxi Normal University, Nanchang, Jiangxi, China; School of Mathematics and Statistics, Shaoguan University, Shaoguan, Guangdong, China 
2  School of Mathematics and Statistics, Jiangxi Normal University, Nanchang, Jiangxi, China 
Pages
1159-1172
Publication year
2022
Publication date
2022
Publisher
De Gruyter Poland
e-ISSN
23915455
Source type
Scholarly Journal
Language of publication
English
DOI
https://doi.org/10.1515/math-2022-0492
ProQuest document ID
2723795498
Copyright
© 2022. This work is published under http://creativecommons.org/licenses/by/4.0 (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.