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Some applications of higher commutators in Mal’cev algebras

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Abstract

We establish several properties of Bulatov’s higher commutator operations in congruence permutable varieties. We use higher commutators to prove that for a finite nilpotent algebra of finite type that is a product of algebras of prime power order and generates a congruence modular variety, affine completeness is a decidable property. Moreover, we show that in such algebras, we can check in polynomial time whether two given polynomial terms induce the same function.

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Authors and Affiliations

  1. Institut für Algebra, Johannes Kepler Universität Linz, 4040, Linz, Austria

    Erhard Aichinger

  2. Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Trg Dositeja Obradovića 4, 21000, Novi Sad, Serbia

    Nebojša Mudrinski

Authors
  1. Erhard Aichinger
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  2. Nebojša Mudrinski
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Correspondence to Erhard Aichinger.

Additional information

Presented by R. Freese.

The second author is supported by Grant No. 144011 of the Ministry of Science of the Republic of Serbia, and the Scholarship ‘One-Month Visits to Austria for University Graduates’ WUS-Austria from the Austrian Ministry of Education, Science and Culture.

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Aichinger, E., Mudrinski, N. Some applications of higher commutators in Mal’cev algebras. Algebra Univers. 63, 367–403 (2010). https://doi.org/10.1007/s00012-010-0084-1

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  • DOI: https://doi.org/10.1007/s00012-010-0084-1

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