Congruences associated with the kernel and the trace operators for primitive regular semigroups

Abstract

The aim of this paper is the study of the semigroup generated by the set of the kemel-trace operators on the congruence lattice of a primitive regular semigroup. Since the structure of the nontrivial primitive regular semigroups is best described as an orthogonal sum of completely 0-simple semigroups, the problem of describing the previous semigroup is solved by determining the semigroups associated with any semigroup of the orthogonal sum. To do the latter, use is made of the Rees Theorem.