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Taylor’s Modularity Conjecture and Related Problems for Idempotent Varieties

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Abstract

We provide a partial result on Taylor’s modularity conjecture, and several related problems. Namely, we show that the interpretability join of two idempotent varieties that are not congruence modular is not congruence modular either, and we prove an analog for idempotent varieties with a cube term. Also, similar results are proved for linear varieties and the properties of congruence modularity, having a cube term, congruence n-permutability for a fixed n, and satisfying a non-trivial congruence identity.

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Acknowledgements

The results of the present paper are a part of the author’s Doctoral Thesis. The author would like to express his gratitude to his advisor, Libor Barto, for his supervision of this work.

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Authors and Affiliations

  1. Department of Algebra, Faculty of Mathematics and Physics, Charles University in Prague, Sokolovská 83, 186 75, Praha, Czech Republic

    Jakub Opršal

  2. Institut für Algebra, Technische Universität Dresden, 01062, Dresden, Germany

    Jakub Opršal

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  1. Jakub Opršal
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Correspondence to Jakub Opršal.

Additional information

Supported by Czech Science Foundation, GACR 13-01832S; and Charles University in Prague, project GAUK-558313. The author has also received funding from the European Research Council (Grant Agreement no. 681988, CSP-Infinity) and the National Science Center Poland under grant no. UMO-2014/13/B/ST6/01812

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Opršal, J. Taylor’s Modularity Conjecture and Related Problems for Idempotent Varieties. Order 35, 433–460 (2018). https://doi.org/10.1007/s11083-017-9441-4

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