The Smallest Proper Congruence on Sandwich Semigroups T(X,Y,θ)
Pei Hui-shen · Advances in Mathematics · 2004
The relationship between the congruences on T(X,Y,θ) and the T~θ-equivalences on the set Y is investigated. The homomorphism C from the congruence lattice C(T(X,Y,θ)) onto the T~θ-equivalence lattice T_(eq)~θ(Y) and the homomorphism γ from T_(eq)~θ(Y) into C(T(X,Y,θ)) are established. And the conditions when there exist the smallest proper T~θ-equivalence on Y and the smallest proper congruence on T(X,Y,θ) are discussed.