The free idempotent generated locally inverse semigroup

TitleThe free idempotent generated locally inverse semigroup
Publication TypePreprint
Year of Preprint2016
AuthorsOliveira L
Abstract

In this paper we construct a model for the free idempotent generated locally inverse semigroup on a set X. The elements of this model are special vertex-labeled bipartite trees with a pair of distinguished vertices. To describe this model, we need first to introduce a variation of a model for the free pseudosemilattice on a set X presented in [3]. A construction of a graph associated with a regular semigroup was presented in [4] in order to give a first example of a free regular idempotent generated semigroup on a biordered set E with non-free maximal subgroups. If G is the graph associated with the free pseudosemilattice on X, we shall see that the models we present for the free pseudosemilattice on X and for the free idempotent generated locally inverse semigroup on X are closely related with the graph G.

[2016-5]

Area / Group: 

Semigroups, Automata and Languages