Expansions of inverse semigroups

Abstract

AbstractWe construct the freest idempotent-pure expansion of an inverse semigroup, generalizing an expansion of Margolis and Meakin for the group case. We also generalize the Birget-Rhodes prefix expansion to inverse semigroups with an application to partial actions of inverse semigroups. In the process of generalizing the latter expansion, we are led to a new class of idempotent-pure homomorphisms which we termF-morphisms. These play the same role in the theory of idempotent-pure homomorphisms thatF-inverse monoids play in the theory ofE-unitary inverse semigroups.