The K°-relation on the Congruence Lattice of a Regular Semigroup with an Inverse Transversal
Ying, Feng, Li -, Мин, Wang · Acta Scientiarum Naturalium Universitatis Sunyatseni · 2012
Let S be a regular semigroup with an inverse transversal S° and C(S) the congruence lattice of S. A relation K° on C(S) is introduced as follows: if ρ, θ∈ C(S), then we say that ρ and θ are K°-related if Ker ρ° = Ker θ° , where ρ° = ρ|S°. Expressions for the least and the greatest congruences in the same K°-class as ρ are provided. A number of equivalent conditions for K° being a congruence are given.