Acta Mathematica Hungarica

, Volume 151, Issue 1, pp 47–49 | Cite as

\({\mathcal{V}_{SI}}\) first order implies \({\mathcal{V}_{DI}}\) first order

Article

Abstract

We prove that if \({\mathcal{V}}\) is a modular variety such that the subdirectly irreducible algebras form a first order class in which there are no trivial subalgebras, then the class of directly indecomposable algebras of \({\mathcal{V}}\) is also first order.

Key words and phrases

Congruence modular variety directly indecomposable algebra first order class 

Mathematics Subject Classification

08B10 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Kollár J.: Congruences and one element subalgebras. Algebra Universalis 9, 266–267 (1979)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Vaggione D.: Varieties of shells. Algebra Universalis 36, 483–487 (1996)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Vaggione D.: Modular varieties with the Fraser–Horn property. Proc. Amer. Math. Soc. 127, 701–708 (1999)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2016

Authors and Affiliations

  1. 1.Facultad de Matemática, Astronomía y FísicaUniversidad Nacional de CórdobaCórdobaArgentina

Personalised recommendations