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GLOBALS OF PSEUDOVARIETIES OF COMMUTATIVE SEMIGROUPS: THE FINITE BASIS PROBLEM, DECIDABILITY AND GAPS

Published online by Cambridge University Press:  20 January 2009

Jorge Almeida  and
Assis Azevedo
Jorge Almeida
Affiliation:
Centro de Matemática, Faculdade de Ciências, Universidade do Porto, 4099-002 Porto, PT
Assis Azevedo
Affiliation:
Centro de Matemática, Universidade do Minho, Braga, PT
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Abstract

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Whereas pseudovarieties of commutative semigroups are known to be finitely based, the globals of monoidal pseudovarieties of commutative semigroups are shown to be finitely based (or of finite vertex rank) if and only if the index is 0, 1 or $\omega$. Nevertheless, on these pseudovarieties, the operation of taking the global preserves decidability. Furthermore, the gaps between many of these globals are shown to be big in the sense that they contain chains which are order isomorphic to the reals.

AMS 2000 Mathematics subject classification: Primary 20M07; 20M05

Keywords

semigroupoidglobal pseudovarietypseudoidentity basis
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 44 , Issue 1 , February 2001 , pp. 27 - 47
Copyright
Copyright © Edinburgh Mathematical Society 2001