Skip to main content
SpringerLink
Log in

Varieties of idempotent slim groupoids

  • Published:
Czechoslovak Mathematical Journal Aims and scope Submit manuscript

Abstract

Idempotent slim groupoids are groupoids satisfying xx ≈ x and x(yz) ≈ xz. We prove that the variety of idempotent slim groupoids has uncountably many subvarieties. We find a four-element, inherently nonfinitely based idempotent slim groupoid; the variety generated by this groupoid has only finitely many subvarieties. We investigate free objects in some varieties of idempotent slim groupoids determined by permutational equations.

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. S. Crvenković and J. Dudek: Rectangular groupoids. Czech. Math. J. 35 (1985), 405–414.

    Google Scholar 

  2. J. A. Gerhard: The lattice of equational classes of idempotent semigroups. J. Algebra 15 (1970), 195–224.

    Article  MATH  MathSciNet  Google Scholar 

  3. E. Jacobs and R. Schwabauer: The lattice of equational classes of algebras with one unary operation. Ann. of Math. 71 (1964), 151–155.

    MATH  MathSciNet  Google Scholar 

  4. J. Ježek: Slim groupoids. To appear.

  5. R. McKenzie, G. McNulty and W. Taylor: Algebras, Lattices, Varieties, Volume I. Wadsworth & Brooks/Cole, Monterey, CA, 1987.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Algebra, Charles University, Sokolovská 83, 186 75, Praha 8, Czech Republic

    J. Ježek

Authors
  1. J. Ježek
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. Ježek.

Additional information

The work is a part of the research project MSM0021620839 financed by MSMT and partly supported by the Grant Agency of the Czech Republic, grant #201/05/0002.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ježek, J. Varieties of idempotent slim groupoids. Czech Math J 57, 1289–1309 (2007). https://doi.org/10.1007/s10587-007-0124-y

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10587-007-0124-y

Keywords

Search

Navigation