Algebra universalis

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

Taylor’s modularity conjecture holds for linear idempotent varieties

  • Wolfram Bentz
  • Luís SequeiraEmail author


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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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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