• A NEW PROOF FOR GANTOS’S THEOREM ON SEMILATTICE OF BISIMPLE INVERSE SEMIGROUPS

Abstract

Gantos has shown that, if  is a semilattice of right cancellative monoids with the (LC) condition and certain further conditions, then we can associate it with a semilattice of bisimple inverse semigroups. We show that one of Gantos’s conditions is equivalent to  itself having the (LC) condition. We use this equivalence to define a simple form for the multiplication which is easier to deal with than the form which Gantos used. We provide a simple proof completely independent of Gantos’s result.