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 p, θ∈ C(S), then we say that p and 0 are K°-...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 p, θ∈ C(S), then we say that p and 0 are K°-related if Ker pO = Ker θ°, where p°= p|s°. Expressions for the least and the greatest congruences in the same K°-class as p are provided. A number of equivalent conditions for K° being a congruence are given.展开更多
文摘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 p, θ∈ C(S), then we say that p and 0 are K°-related if Ker pO = Ker θ°, where p°= p|s°. Expressions for the least and the greatest congruences in the same K°-class as p are provided. A number of equivalent conditions for K° being a congruence are given.