Skip to main content
SpringerLink
Log in

Minimal non-permutative pseudovarieties of semigroups III

  • Published:
algebra universalis Aims and scope Submit manuscript

Abstract

Various types of permutativity conditions are important in the study of (pseudo)varieties of semigroups. In previous papers of this series, minimal pseudovarieties failing certain permutativity conditions were determined. This theme is pursued here in relation to a family of conditions which appear in the investigation of power pseudovarieties of semigroups, namely, for eachk≥0, we consider the conditionC k on a semigroup that it satisfy the identityx 1 ...x k y 1 y 2 z 1 ...z n=x 1 ...x k y 2 y 1 z 1 ...z n for somen. For all minimal pseudovarieties failing Ck, a generator and finite basis of identities are specified.

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

Similar content being viewed by others

References

  1. J.Almeida,Minimal non-permutative pseudovarieties of semigroups I, to appear in Pacific J. of Math. Vol. 121 (1986).

  2. J.Almeida,Minimal non-permutative pseudovarieties of semigroups II, to appear in Pacific J. of Math. Vol. 121. (1986).

  3. J.Almeida,Power pseudovarieties of semigroups I, manuscript, Universidade do Minho.

  4. J.Almeida,Power pseudovarieties of semigroups II, manuscript, Universidade do Minho.

  5. C. J.Ash,Pseudovarieties, generalized varieties and similarly described classes, to appear in J. Algebra.

  6. A. H.Clifford and G. B.Preston,The Algebraic Theory of Semigroups, Vol. 1 and 2, Amer. Math. Soc, Math. Surveys 7, Providence, R. I., 1961, 1967.

  7. G. Laixement,Semigroups and Combinatorial Applications, Wiley-Interscience, New York, 1979.

    Google Scholar 

  8. S. W. Margolis andJ. E. Pin,Minimal non-commutative varieties and power varieties, Pacific J. of Math.111 (1984) 125–135.

    Google Scholar 

  9. G. Pöllak,On the consequences of permutation identities, Acta Sci. Math.34 (1973) 323–333.

    Google Scholar 

  10. M. S. Putcha andA. Yaqub,Semigroups satisfying permutation identities, Semigroup Forum3 (1971) 68–73.

    Google Scholar 

  11. V. V. Rasin,On the lattice of varieties of completely simple semigroups, Semigroup Forum17 (1979) 113–122.

    Google Scholar 

  12. L. Rédei,Algebra, Vol.1 (English translation), Pergamon Press, Oxford, 1967.

    Google Scholar 

  13. J. Reiterman,The Birkhoff theorem for finite algebras, Algebra Universalis14 (1982) 1–10.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Universidade do Minho, Braga, Portugal

    Jorge Almeida

Authors
  1. Jorge Almeida
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was supported, in part, by NSERC Grant A4044.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Almeida, J. Minimal non-permutative pseudovarieties of semigroups III. Algebra Universalis 21, 256–279 (1985). https://doi.org/10.1007/BF01188061

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01188061

Keywords

Search

Navigation