Semigroups with atomistic congruence lattices
Karl Auinger · Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 1992
Abstract In this note a characterization of semigroups with atomistic consruence lattices, given for weakly reductive semigroups, is generalized to arbitrary semigroups. Also, it is shown that there is a complete congruence on the congruence lattice of such a semigroup that decomposes it into a disjoint union of intervals of the partition lattice.