Some remarkable congruences on completely regular semigroups
A completely regular semigroup \(S\) is expressed as \((Y;S_\alpha)\) thereby indicating that \(S\) is a semilattice \(Y\) of completely simple semigroups \(S_\alpha\). For each pair \(\alpha,\beta\in Y\), \(\alpha>\beta\), let \(\kappa_{\alpha,\beta}\) be the congruence on \(S\) generated by the pairs \((a,b)\), \(a\in S_\alpha\), \(b\in S_\beta\), \(a>b\). It is shown that these congruences play a crucial role in finding conditions which ensure that the kernel relation \(K\) on the congruence lattice \(C(S)\) be a congruence. Further the author introduces a generalization of Rees congruences by involving two ideals of \(S\) and a congruence on \(S\). For a fixed congruence, this produces a lattice of congruences on \(S\) with several interesting properties.
scientific article; zbMATH DE number 1309888