| Issue |
RAIRO-Theor. Inf. Appl.
Volume 39, Number 1, January-March 2005
Imre Simon, the tropical computer scientist
|
|
|---|---|---|
| Page(s) | 1 - 29 | |
| DOI | https://doi.org/10.1051/ita:2005001 | |
| Published online | 15 March 2005 | |
The globals of pseudovarieties of ordered semigroups containing B2 and an application to a problem proposed by Pin
1
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.
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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