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Algebra universalis

, Volume 71, Issue 2, pp 101–107 | Cite as

Taylor’s modularity conjecture holds for linear idempotent varieties

  • Wolfram Bentz
  • Luís Sequeira
Article

Abstract

The “Modularity Conjecture” is the assertion that the join of two nonmodular varieties in the lattice of interpretability types is nonmodular. We establish the veracity of this conjecture for the case of linear idempotent varieties. We also establish analogous results concerning n-permutability for some n, and the satisfaction of nontrivial congruence identities.

2010 Mathematics Subject Classification

Primary: 08B10 Secondary: 08B05 03C05 

Key words and phrases

interpretability lattice congruence modularity derivative linear variety 

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References

  1. 1.
    Bentz W.: A characterization of Hausdorff separation for a special class of varieties. Algebra Universalis 55, 259–276 (2006)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Bentz W.: A Characterization of T 3 Separation for a Special Class of Varieties. Algebra Universalis 56, 399–410 (2007)CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Dent A., Kearnes K., Szendrei A.: An easy test for congruence modularity. Algebra Universalis 67, 375–392 (2012)CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Freese, R.: Equations implying congruence n-permutability and semidistributivity. Algebra Universalis (to appear)Google Scholar
  5. 5.
    Garcia,O., Taylor, W.: The Lattice of Interpretability Types of Varieties. Mem. Amer. Math. Soc., vol. 50, Number 305 (1984)Google Scholar
  6. 6.
    Kelly D.: Basic equations: word problems and Mal’cev conditions. Notices Amer. Math. Soc. 20, A–54 (1973)Google Scholar
  7. 7.
    Neumann W. D.: On Mal’cev conditions. J. Austral. Math. Soc. 17, 376–384 (1974)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Sequeira, L.: Maltsev Filters. PhD thesis, Universidade de Lisboa (2001) http://webpages.fc.ul.pt/~lfsequeira/math/tese.pdf
  9. 9.
    Sequeira L.: Near-unanimity is decomposable. Algebra Universalis 50, 157–164 (2003)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Sequeira L.: On the modularity conjecture. Algebra Universalis 55, 495–508 (2006)CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    Taylor W.: Simple equations on real intervals. Algebra Universalis 61, 213–226 (2009)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Tschantz, S.: Congruence permutability is join prime (manuscript)Google Scholar

Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Centro de ÁlgebraUniversidade de LisboaLisboaPortugal
  2. 2.Departamento de Matemática, Faculdade de CiênciasUniversidade de LisboaLisboaPortugal

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