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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

Oliveira, Luís
Semigroup Forum , Volume 96 (3) – Jul 12, 2017
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22 pages

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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 Forum – Springer Journals

Published: Jul 12, 2017

References

  • Finite Semigroups and Universal Algebra
    Almeida, J
  • The bifree locally inverse semigroup on a set
    Auinger, K
  • On the lattice of existence varieties of locally inverse semigroups
    Auinger, K
  • On the variety of strict pseudosemilattices
    Auinger, K; Oliveira, L
  • Subgroups of free idempotent generated semigroups need not be free
    Brittenham, M; Margolis, S; Meakin, J
  • Every group is a maximal subgroup of the free idempotent generated semigroup over a band
    Dolinka, I; Ruškuc, N
  • Biordered sets come from semigroups
    Easdown, D
  • On finite 0-simple semigroups and graph theory
    Graham, RL
  • On maximal subgroups of free idempotent generated semigroups
    Gray, R; Ruskuc, N
  • Maximal subgroups of free idempotent-generated semigroups over the full transformation monoid
    Gray, R; Ruškuc, N
  • Identities for existence varieties of regular semigroups
    Hall, T
  • Completely 0-simple semigroups and their associated graphs and groups
    Houghton, CH
  • Fundamentals of Semigroup Theory
    Howie, J
  • A new approach in the theory of orthodox semigroups
    Kaďourek, J; Szendrei, MB
  • Demi-groupes reguliers
    Lallement, G
  • Pseudo-semilattices and biordered sets I
    Nambooripad, KSS
  • Subgroups of free idempotent generated regular semigroups
    Nambooripad, KSS; Pastijn, F
  • Idempotent generated completely 0-simple semigroups
    Pastijn, F
  • The biorder on the partial groupoid of idempotents of a semigroup
    Pastijn, F
  • Maximal dense ideal extensions of locally inverse semigroups
    Pastijn, F; Oliveira, L