Issue Theoret. Informatics Appl. Volume 39, Number 1, January-March 2005 Imre Simon, the tropical computer scientist Page(s) 1 - 29 DOI 10.1051/ita:2005001

Theoret. Informatics Appl. 39, 1-29 (2005)
DOI: 10.1051/ita:2005001

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

Jorge Almeida¹ and Ana P. Escada<sup>2

1</sup>  Centro de Matemática, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal; jalmeida@fc.up.pt
²  Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade de Coimbra, Apartado 3008, 3001-454 Coimbra, Portugal.

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.

Mathematics Subject Classification. 20M05, 20M07, 20M35

Key words: Semigroup -- pseudovariety -- semigroupoid -- category -- pseudoidentity -- dot-depth -- concatenation hierarchies.


© EDP Sciences 2005

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