Hostname: page-component-8448b6f56d-dnltx Total loading time: 0 Render date: 2024-04-24T08:28:31.977Z Has data issue: false hasContentIssue false
  • English
  • Français

Idempotent-generated semigroups and pseudovarieties

Part of: Semigroups

Published online by Cambridge University Press:  20 June 2011

J. Almeida  and
A. Moura
J. Almeida
Affiliation:
Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal (jalmeida@fc.up.pt)
A. Moura
Affiliation:
Laboratório de Engenharia Matemática, Instituto Superior de Engenharia do Porto, Rua Dr António Bernardino de Almeida 431, 4200-072 Porto, Portugal and Centro de Matemática, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal (aim@isep.ipp.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.

The operator that constructs the pseudovariety generated by the idempotent-generated semi-groups of a given pseudovariety is investigated. Several relevant examples of pseudovarieties generated by their idempotent-generated elements are given, as well as some properties of this operator. Particular attention is paid to the pseudovarieties in {J, R, L, DA} concerning this operator and their generator ranks and idempotent-generator ranks.

Keywords

finite semigrouppseudovarietyoperatoridempotent-generated semigroupgenerator rankidempotent generator rank

MSC classification

Secondary: 20M07: Varieties and pseudovarieties of semigroups
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 54 , Issue 3 , October 2011 , pp. 545 - 568
Copyright
Copyright © Edinburgh Mathematical Society 2011

References

1.Almeida, J., Finite semigroups and universal algebra (World Scientific, 1994).Google Scholar
2.Almeida, J., Profinite semigroups and applications, in Structural theory of automata, semigroups, and universal algebra (ed. Kudryavtsev, V. B. and Rosenberg, I. G.), NATO Science Series II: Mathematics, Physics and Chemistry, Volume 207, pp. 1–45 (Springer, 2005).Google Scholar
3.Almeida, J. and Weil, P., Free profinite R-trivial monoids, Int. J. Alg. Comput. 7 (1997), 625–671.CrossRefGoogle Scholar
4.Auinger, K., Hall, T. E., Reilly, N. R. and Zhang, S., Congruences on the lattice of pseudovarieties of finite semigroups, Int. J. Alg. Comput. 7 (1997), 433–455.CrossRefGoogle Scholar
5.Benzaken, C. and Mayr, H. C., Notion de demi-bande, demi-bandes de type deux, Semigroup Forum 10 (1975), 115–128.Google Scholar
6.Eilenberg, S., Automata, languages and machines, Volume B (Academic Press, New York, 1976).Google Scholar
7.Gomes, G. and Howie, J., On the ranks of certain finite semigroups of transformations, Math. Proc. Camb. Phil. Soc. 101 (1987), 395–403CrossRefGoogle Scholar
8.Howie, J. M., The subsemigroup generated by the idempotents of a full transformation semigroup, J. Lond. Math. Soc. 41 (1966), 707–716.CrossRefGoogle Scholar
9.Howie, J. M., Products of idempotents in certain semigroups of order-preserving transformations, Proc. Edinb. Math. Soc. 17 (1971), 223–236.CrossRefGoogle Scholar
10.Laradji, A. and Umar, A., On certain finite semigroups of order-decreasing transformations, I, Semigroup Forum 69 (2004), 184–200.CrossRefGoogle Scholar
11.Moura, A., E-local pseudovarieties, Technical Report CMUP 2009-45, University of Porto (2009) (available at http://cmup.fc.up.pt/cmup/amoura/AMoura_Elocalpv.pdf).Google Scholar
12.Moura, A., Representations of the free profinite object over DA, Int. J. Alg. Comput. in press (DOI:10.1142/S0218196711006467).Google Scholar
13.Pastijn, F., Embedding semigroups in semibands, Semigroup Forum 14 (1977), 247–263.CrossRefGoogle Scholar
14.Petrich, M., Embedding semigroups into idempotent generated ones, Monatsh. Math. 141 (2004), 315–322.CrossRefGoogle Scholar
15.Pin, J.-E., Varieties of formal languages (Plenum, London, 1986).CrossRefGoogle Scholar
16.Reilly, N. R. and Zhang, S., Operators on the lattice of pseudovarieties of finite semigroups, Semigroup Forum 57 (1998), 208–239.CrossRefGoogle Scholar
17.Reiterman, J., The Birkhoff theorem for finite algebras, Alg. Univers. 14 (1982), 1–10.Google Scholar
18.Rosenstein, J. G., Linear orderings (Academic Press, New York, 1982).Google Scholar
19.Straubing, H., On finite -trivial monoids, Semigroup Forum 19 (1980), 107–110.CrossRefGoogle Scholar
20.Umar, A., On the semigroups of order-decreasing finite full transformations, Proc. R. Soc. Edinb. A 120 (1992), 129–142.CrossRefGoogle Scholar
21.Umar, A., On the ranks of certain finite semigroups of order-decreasing transformations, Portugaliae Math. 53 (1996), 23–32.Google Scholar