Algebra universalis

, Volume 70, Issue 4, pp 327–345 | Cite as

Varieties with equationally definable factor congruences



A variety has definable factor congruences if there is a first order formula φ which defines each factor congruence in terms of its associated central element. We study the case in which φ is a conjunction of equations.

2010 Mathematics Subject Classification

Primary: 03C05 Secondary: 08B05 08B10 

Keywords and phrases

central element equationally definable factor congruences Boolean factor congruences 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bigelow D., Burris S.: Boolean algebras of factor congruences. Acta Sci. Math. (Szeged) 54, 11–20 (1990)MathSciNetMATHGoogle Scholar
  2. 2.
    Burris, S., Sankappanavar, H.: A course in Universal Algebra. Springer-Verlag, New York (1981)CrossRefMATHGoogle Scholar
  3. 3.
    Gumm, H.P.: Geometrical Methods in Congruence Modular Varieties. Mem. Amer. Math. Soc., vol. 45, 286, (1983)Google Scholar
  4. 4.
    Kollar J.: Congruences and one element subalgebras. Algebra Universalis 9, 266–267 (1979)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Sanchez Terraf, P.: Existentially definable factor congruences. Acta Sci. Math. (Szeged) 76, 49–54 (2010)MathSciNetMATHGoogle Scholar
  6. 6.
    Sanchez Terraf, P., Vaggione, D.: Varieties with definable factor congruences. Trans. Amer. Math. Soc. 361, 5061–5088 (2009)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Vaggione, D.: Varieties in which the Pierce stalks are directly indecomposable. J. Algebra 184, 424–434 (1996)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Vaggione, D.: Varieties of shells. Algebra Universalis 36, 483–487 (1996)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Vaggione, D.: Modular varieties with the Fraser-Horn property. Proc. Amer. Math. Soc. 127 No. 3, 701–708 (1998)Google Scholar
  10. 10.
    Vaggione, D.: Central elements in varieties with the Fraser-Horn property. Adv. Math. 148, 193–202 (1999)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Facultad de MatemáticaAstronomía y Física (Fa.M.A.F.) Universidad Nacional de Córdoba - Ciudad UniversitariaCórdobaArgentina

Personalised recommendations