A Munn Type Representation for a Class of E-Semiadequate Semigroups,

Munnʹs construction of a fundamental inverse semigroup TE from a semilattice E provides an important tool in the study of inverse semigroups. We present here a semigroup FE that plays for a class of E-semiadequate semigroups the role that TE plays for inverse semigroups. Every inverse semigroup with semilattice of idempotents E is E-semiadequate. There are however many interesting E-semiadequate semigroups that are not inverse, we consider various such examples arising from Schützenberger products.