Relatively congruence-free regular semigroups.
Let \(\tau\) be an equivalence relation on a semigroup \(S\). According to \textit{H. Yu} et al. [Semigroup Forum 84, No. 2, 308-322 (2012; Zbl 1257.20057)], \(S\) is called \(\tau\)-congruence-free if any congruence \(\rho\) on \(S\) is either disjoint from \(\tau\) or contains \(\tau\). Let \(\tau\) be one of Green's relations: \(\mathcal J\), \(\mathcal L\), \(\mathcal R\). In these cases, \(\tau\)-congruence-free regular semigroups are characterized, modulo congruence-free regular semigroups. If \(S\) is a completely semisimple semigroup, a complete characterization is obtained for the mentioned values of \(\tau\) and also for the case \(\tau=\mathcal H\).
scientific article; zbMATH DE number 6385106
scientific article