Skip to main content

Advertisement

SpringerLink
Log in

E-local pseudovarieties

  • RESEARCH ARTICLE
  • Published:
Semigroup Forum Aims and scope Submit manuscript

Abstract

Generalizing a property of the pseudovariety of all aperiodic semigroups observed by Tilson, we call E -local a pseudovariety V which satisfies the following property: for a finite semigroup, the subsemigroup generated by its idempotents belongs to V if and only if so do the subsemigroups generated by the idempotents in each of its regular \(\mathcal{D}\)-classes. In this paper, we present several sufficient or necessary conditions for a pseudovariety to be E-local or for a pseudoidentity to define an E-local pseudovariety. We also determine several examples of the smallest E-local pseudovariety containing a given pseudovariety.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  1. Almeida, J.: Finite Semigroups and Universal Algebra. World Scientific, Singapore (1994). English translation

    MATH  Google Scholar 

  2. Almeida, J., Moura, A.: Idempotent-generated semigroups and pseudovarieties. Proc. Edinb. Math. Soc. 54, 545–568 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  3. Almeida, J., Volkov, M.V.: Profinite identities for finite semigroups whose subgroups belong to a given pseudovariety. J. Algebra Appl. 2, 137–163 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  4. Fitz-Gerald, D.G.: On inverses of products of idempotents in regular semigroups. J. Aust. Math. Soc. 13, 335–337 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  5. Graham, R.: On finite 0-simple semigroups and graph theory. Math. Syst. Theory 2, 325–339 (1968)

    Article  MATH  Google Scholar 

  6. Pin, J.-E.: Varieties of Formal Languages. Plenum, London (1986). English translation

    Book  MATH  Google Scholar 

  7. Pin, J.-E.: PG=BG, a success story. In: Fountain, J. (ed.) NATO Advanced Study Institute Semigroups, Formal Languages and Groups, pp. 33–47. Kluwer Academic, Dordrecht (1995)

    Google Scholar 

  8. Reiterman, J.: The Birkhoff theorem for finite algebras. Algebra Univers. 14, 1–10 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  9. Rhodes, J., Steinberg, B.: The q-Theory of Finite Semigroups. Springer, New York (2009)

    Book  Google Scholar 

  10. Tilson, B.: Complexity of two J-class semigroups. Adv. Math. 11, 215–237 (1973)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The author is grateful to the anonymous referee for warning a flaw in the proof of the initially statement of Theorem 3.11. This work is part of the author’s doctoral thesis, written under the supervision of Prof. Jorge Almeida, from whose advice the author has greatly benefited. This work was supported by Fundação para a Ciência e a Tecnologia (FCT) through the PhD Grant SFRH/BD/19720/2004, through the Centro de Matemática da Universidade do Porto (CMUP) and also through the project PTDC/MAT/65481/2006, which is partly funded by the European Community Fund FEDER.

Author information

Authors and Affiliations

  1. Instituto Superior de Engenharia do Porto/LEMA and Centro de Matemática da Universidade do Porto, Rua do Campo Alegre, 687, 4169-007, Porto, Portugal

    A. Moura

Authors
  1. A. Moura
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Moura.

Additional information

Communicated by Jean-Eric Pin.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Moura, A. E-local pseudovarieties. Semigroup Forum 85, 169–181 (2012). https://doi.org/10.1007/s00233-012-9413-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00233-012-9413-3

Keywords

Search

Navigation