Skip to main content
SpringerLink
Log in

The weak hereditary class of a variety

  • Published:
Czechoslovak Mathematical Journal Aims and scope Submit manuscript

Abstract

We study the weak hereditary class S w (

) of all weak subalgebras of algebras in a total variety

}. We establish an algebraic characterization, in the sense of Birkhoff’s HSP theorem, and a syntactical characterization of these classes. We also consider the problem of when such a weak hereditary class is weak equational.

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. H. Andréka, I. Németi: Generalization of the concept of variety and quasivariety to partial algebras through category theory. Dissertationes Math. (Rozpr. Matem.) 204, (1983).

  2. P. Burmeister: A Model Theoretic Approach to Partial Algebras. Math. Research 32. Akademie-Verlag, Berlin, 1986.

    Google Scholar 

  3. G. Grätzer, E. T. Schmidt: Characterizations of congruence lattices of abstract algebras. Acta Sci. Math. (Szeged) 24 (1963), 34–59.

    MATH  MathSciNet  Google Scholar 

  4. D. Jakubíková-Studenovská: On completions of partial monounary algebras. Czechoslovak Math. J. 38 (1988), 256–268.

    MATH  MathSciNet  Google Scholar 

  5. M. Llabrés, F. Rosselló: Pushout complements for arbitrary partial algebras. In: Proc. 6th International Workshop on Theory and Application of Graph Transformation TAGT’98. Lect. Notes in Comp. Sc. 1764. 2000, pp. 131–144.

  6. J. Schmidt: A homomorphism theorem for partial algebras. Colloq. Math. 21 (1970), 5–21.

    MATH  MathSciNet  Google Scholar 

  7. B. Staruch, B. Staruch: Strong regular varieties of partial algebras. Alg. Univ. 31 (1994), 157–176.

    Article  MATH  MathSciNet  Google Scholar 

  8. R. Szymański: Decidability of weak equational theories. Czechoslovak Math. J. 46 (1996), 629–664.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Inst. Matematyki, Uniw. Warszawski, ul. Banacha 2, 02-097, Warszawa, Poland

    Wiktor Bartol

  2. Dept. Matemàtiques i Informàtica, Univ. Illes Balears, 07122, Palma de Mallorca, Spain

    Francesc Rosselló

Authors
  1. Wiktor Bartol
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Francesc Rosselló
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bartol, W., Rosselló, F. The weak hereditary class of a variety. Czech Math J 56, 697–710 (2006). https://doi.org/10.1007/s10587-006-0049-x

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10587-006-0049-x

Keywords

Search

Navigation