The free idempotent generated locally inverse semigroup

• Type: Article in International Scientific Journal
• Date: 2018

Authors

Luís Oliveira (Author) FCUP

Journal

Title: Semigroup Forum

Vol. 96

Pages: 452-473

ISSN: 0037-1912

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 2 Citations

Scopus - 0 Citations

Scientific classification

CORDIS: Physical sciences > Mathematics

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-00N-3RD

DOI: 10.1007/s00233-017-9882-5

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 22