Congruences on Completely Regular Semigroups

There are two subjects in the literature on semigroups which have recently attracted great attention: the class of completely regular semigroups (that is semigroups which are unions of their subgroups) and congruences on regular semigroups. In completely regular semigroups, the most popular subject is that of varieties, even though other aspects of them, such as structure, congruences, amalgamation, received their due attention. On the other hand, the treatment of congruences on regular semigroups became especially interesting with the emergence of the kernel-trace approach. This method proved quite successful in the case of inverse semigroups, see [6], whereas the analysis for the general regular semigroups encounters considerable difficulties, see [4].