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RAIRO - Theoretical Informatics and Applications (1)

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The globals of pseudovarieties of ordered semigroups containing B2 and an application to a problem proposed by Pin
Jorge Almeida, Ana P. Escada
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 39 / Issue 1 / January 2005

Published online by Cambridge University Press:

15 March 2005, pp. 1-29

Print publication:

January 2005
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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.