Congruences on glrac semigroups (I)
Haijun Liu, Xiaojiang Guo · Journal of Algebra and Its Applications · 2021
The theory of congruences on semigroups is an important part in the theory of semigroups. The aim of this paper is to study (2,1)-congruences on a glrac semigroup. It is proved that the (2,1)-congruences on a glrac semigroup become a complete sublattice of its lattice of congruences. Especially, the structures of left restriction semigroup (2,1)-congruences and the projection-separating (2,1)-congruences on a glrac semigroup are established. Also, we demonstrate that they are both complete sublattice of (2,1)-congruences and consider their relations with respect to complete lattice homomorphism.