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The globals of pseudovarieties of ordered semigroups containing B2 and an application to a problem proposed by Pin

Published online by Cambridge University Press:  15 March 2005

Jorge Almeida  and
Ana P. Escada
Jorge Almeida
Affiliation:
Centro de Matemática, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal; jalmeida@fc.up.pt
Ana P. Escada
Affiliation:
Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade de Coimbra, Apartado 3008, 3001-454 Coimbra, Portugal.
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Abstract

Given a basis of pseudoidentities for a pseudovariety of ordered semigroups containing the 5-element aperiodic Brandt semigroup B2, under the natural order, it is shown that the same basis, over the most general graph over which it can be read, defines the global. This is used to show that the global of the pseudovariety of level 3/2 of Straubing-Thérien's concatenation hierarchy has infinite vertex rank.

Keywords

Semigrouppseudovarietysemigroupoidcategorypseudoidentitydot-depthconcatenation hierarchies.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 39 , Issue 1: Imre Simon, the tropical computer scientist , January 2005 , pp. 1 - 29
Copyright
© EDP Sciences, 2005

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