Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-26T07:26:12.033Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Almeida, J. and Costa, A., ‘Infinite-vertex free profinite semigroupoids and symbolic dynamics’, J. Pure Appl. Algebra 213 (2009), 605–631.CrossRefGoogle Scholar
Almeida, J. and Trotter, P. G., ‘The pseudoidentity problem and reducibility for completely regular semigroups’, Bull. Aust. Math. Soc. 63 (2001), 407–433.CrossRefGoogle Scholar
Almeida, J. and Weil, P., ‘Profinite categories and semidirect products’, J. Pure Appl. Algebra 123 (1998), 1–50.CrossRefGoogle Scholar
Jones, P. R., ‘Profinite categories, implicit operations and pseudovarieties of categories’, J. Pure Appl. Algebra 109 (1996), 61–95.CrossRefGoogle Scholar
Rhodes, J. and Steinberg, B., ‘Profinite semigroups, varieties, expansions and the structure of relatively free profinite semigroups’, Internat. J. Algebra Comput. 11 (2002), 627–672.CrossRefGoogle Scholar
Rhodes, J. and Steinberg, B., The q-Theory of Finite Semigroups, Springer Monographs in Mathematics (Springer, New York, 2009).CrossRefGoogle Scholar
Ribes, L., Grupos profinitos y grafos topológicos, Publicacions de la Secció de Matemàtiques, 4 (Universitat Autònoma de Barcelona, Barcelona, 1977), 1–64.Google Scholar
Ribes, L. and Zalesskiĭ, P. A., Profinite Groups, Ergebnisse der Mathematik und ihrer Grenzgebiete, Ser. 3, 40 (Springer, Berlin, 2000).CrossRefGoogle Scholar
Willard, S., General Topology (Addison-Wesley, Reading, MA, 1970).Google Scholar