Free Strict Inverse Semigroups

Abstract

A strict inverse semigroup can be constructed by means of the partially ordered set X = S/ J of its principal ideals, its J -classes which are the non-zero parts of Brandt semigroups, and partial homomorphisms between these partial semigroups. The free object in a variety of strict inverse semigroups is described in terms of these parameters. The associated partial order is realized as a set of symmetric and transitive relations on a certain set, and the corresponding Brandt semigroups as well as the partial homomorphisms can be obtained in a canonical way. As an application, a simple solution of the word problem in the free combinatorial strict inverse semigroup is presented.