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The free idempotent generated locally inverse semigroup

The free idempotent generated locally inverse semigroup 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 Auinger and Oliveira (On the variety of strict pseudosemilattices. Stud Sci Math Hungarica 50:207–241, 2013). A construction of a graph associated with a regular semigroup was presented in Brittenham et al. (Subgroups of free idempotent generated semigroups need not be free. J Algebra 321:3026–3042, 2009) 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Semigroup Forum Springer Journals

The free idempotent generated locally inverse semigroup

Semigroup Forum , Volume 96 (3) – Jul 12, 2017

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer Science+Business Media, LLC
Subject
Mathematics; Algebra
ISSN
0037-1912
eISSN
1432-2137
DOI
10.1007/s00233-017-9882-5
Publisher site
See Article on Publisher Site

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 Auinger and Oliveira (On the variety of strict pseudosemilattices. Stud Sci Math Hungarica 50:207–241, 2013). A construction of a graph associated with a regular semigroup was presented in Brittenham et al. (Subgroups of free idempotent generated semigroups need not be free. J Algebra 321:3026–3042, 2009) 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.

Journal

Semigroup ForumSpringer Journals

Published: Jul 12, 2017

References