Skip to main content
SpringerLink
Log in

Definability in the lattice of equational theories of semigroups

  • Research Article
  • Published:
Semigroup Forum Aims and scope Submit manuscript

Abstract

We study first-order definability in the latticeL of equational theories of semigroups. A large collection of individual theories and some interesting sets of theories are definable inL. As examples, ifT is either the equational theory of a finite semigroup or a finitely axiomatizable locally finite theory, then the set {T, T ϖ} is definable, whereT ϖ is the dual theory obtained by inverting the order of occurences of letters in the words. Moreover, the set of locally finite theories, the set of finitely axiomatizable theories, and the set of theories of finite semigroups are all definable.

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. Iskander, A. A.,Coverings in the lattice of varieties, Colloquia Mathematica Societatis János Boyal17. North-Holland, Amsterdam, 1977, pp. 189–203.

    Google Scholar 

  2. Ježek, J.,The lattice of equational theories Part I: Modular elements, Czech. Math. J.31 (1981), 127–152; Part II:The lattice of full sets of terms, Czech. Math. J.31 (1981), 573–603; Part III:Definability and automorphisms, Czech. Math. J.32 (1982), 129–164; Part IV:Equational theories of finite algebras, Czech. Math. J.36 (1986), 331–341.

    Google Scholar 

  3. McKenzie, R.,Definability in lattices of equational theories, Annals of Math. Logic3 (1971), 197–237.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Hawaii, 96822, Honolulu, Hawaii

    Jaroslav Ježek & Ralph McKenzie

  2. Department of Mathematics, University of California, 94720, Berkeley, California

    Jaroslav Ježek & Ralph McKenzie

Authors
  1. Jaroslav Ježek
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ralph McKenzie
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by N. Reilly

The research of both authors was supported by National Science Foundation Grant No. DMS-8302295

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ježek, J., McKenzie, R. Definability in the lattice of equational theories of semigroups. Semigroup Forum 46, 199–245 (1993). https://doi.org/10.1007/BF02573566

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02573566

Keywords

Search

Navigation