The lattice of (2, 1)-congruences on a left restriction semigroup
Haijun Liu, Xiaojiang Guo · Open Mathematics · 2022
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 -, K K -, t t -, and T 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.