The semigroup generated by certain operators on the congruence lattice of a Clifford semigroup
For any congruence relation \(\rho\) on a regular semigroup \(S\), let \(\rho K\) and \(\rho k\) be the greatest and the least congruences on \(S\) with the same kernel as \(\rho\), and, \(\rho T\) and \(\rho t\) the greatest and the least congruences on \(S\) with the same trace as \(\rho\). The semigroup generated by the set \(\Gamma=\{k,K,t,T\}\) of transformations of the congruence lattice of \(S\) is denoted by \(\Omega(S)\). The author finds a finitely presented semigroup \(\Omega=\langle\Gamma\mid\Sigma\rangle\) which has the following property: if \(S\) is any Clifford semigroup, then \(\Omega(S)\) is a homomorphic image of \(\Omega\). An example is given of a Clifford semigroup where \(\Omega\cong\Omega(S)\). The semigroup \(\Omega\) has 19 elements.
scientific article; zbMATH DE number 126123