a1 Deparamento de Matemática, Universidade do Porto, 4000 Porto, Portugal
a2 Department of Mathematics, University of Glasgow, Glasgow G12 8QW
Some new concepts are introduced, in particular that of a unique factorization semilattice. Necessary and sufficient conditions are given for two principal ideals of the semilattice of idempotents of a free inverse monoid FIM(X) to be isomorphic and some properties of the Munn semigroup of E[FIM(X)] are obtained. Some results on the embedding of semilattices in E[FIM(X)] are also obtained.
(Received November 12 1991)