Congruences contained in an equivalence on a semigroup
Peter R. Jones · Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 1980
Abstract The main theorem of this paper shows that the lattice of congruences contained is some equivalence π on a semigroup S can be decomposed into a subdirect product of sublattices of the congruence lattices on the ‘prinipal π-facotrsρ of S—the semigroups formed by adjoining zeroes to the π-classes—whenever these are well-defined. The theorem is then applied to various equavalences and classes of semigroups to give some new results and alternative proofs of known ones.