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

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 kk-, KK-, tt-, and TT-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.

Keywords

• left restriction semigroups
• semilattices
• projection kernel-traces
• (2, 1)-congruences
• complete lattices
• 20m10
• 20m75