A CLASS OF INVERSE SEMIGROUPS WITH BOOLEAN CONGRUENCE LATTICES

Abstract

A construction of inyerse semigroups whose idempotents form a (locally finite) tree and whose congruence lattices have the property P is given where P stands for one of the fol- lowing properties of lattices: (dually) sectionally complemented, relatively complemented, modular and complemented, Boolean, respectively. These semigroups are completely character- ized up to: congruence-free inverse semigroups (without zero), simple groups and locally finite trees. Furthermore, special sublattices of the congruence lattice easily can be studied: any two trace classes are isomorphic, and the lattices of all semilattice congruences and idempotent pure congruences, respectively are Boolean.