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A NOTE ON PSEUDOVARIETIES OF COMPLETELY REGULAR SEMIGROUPS

Part of: Topological and differentiable algebraic systems Semigroups

Published online by Cambridge University Press:  16 June 2015

JORGE ALMEIDA  and
ALFREDO COSTA
JORGE ALMEIDA*
Affiliation:
CMUP, Departamento de Matemática, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal email jalmeida@fc.up.pt
ALFREDO COSTA
Affiliation:
CMUC, Department of Mathematics, University of Coimbra, 3001-501 Coimbra, Portugal email amgc@mat.uc.pt
*
✉jalmeida@fc.up.pt
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Abstract

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A paper of Almeida and Trotter [‘The pseudoidentity problem and reducibility for completely regular semigroups’, Bull. Aust. Math. Soc.63 (2001), 407–433] makes essential use of free profinite semigroupoids over profinite graphs with infinitely many vertices. It has since been shown that such structures must be handled with great care. In this note, it is verified that the required properties hold for the profinite graphs considered by Almeida and Trotter, thereby filling the gaps in the proof.

Keywords

completely regular semigroupspseudovarietiesfree profinite semigroupsfree profinite semigroupoidsprofinite graphs

MSC classification

Primary: 20M07: Varieties and pseudovarieties of semigroups
Secondary: 20M17: Regular semigroups 20M05: Free semigroups, generators and relations, word problems 22A15: Structure of topological semigroups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 92 , Issue 2 , October 2015 , pp. 233 - 237
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

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