A Munn type representation for a class of E-semiadequate semigroups

Munn's construction of a fundamental inverse semigroup T-E from a semilatti ce E provides an important tool in the study of inverse semigroups. We pres ent here a semigroup F-E that plays for a class of E-semiadequate semigroup s the role that T-E plays for inverse semigroups. Every inverse semigroup w ith semilattice of idempotents E is E-semiadequate. There are however many interesting E-semiadequate semigroups that are not inverse, we consider var ious such examples arising from Schutzenberger products. (C) 1999 Academic Press.