On unique factorization semilattices

The class of unique factorization semilattices (UFSs) contains important examples of semilattices such as free semilattices and the semilattices of idempotents of free inverse monoids. Their structural properties allow an efficient study, among other things, of their principal ideals. A general construction of UFSs from arbitrary posets is presented and some categorical properties are derived. The problem of embedding arbitrary semilattices into UFSs is considered and complete characterizations are obtained for particular classes of semilattices. The study of the Munn semigroup for regular UFSs is developed and a complete characterization is accomplished with respect to being E-unitary.