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Representing subalgebras as retracts of finite subdirect powers

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Abstract

We prove that if \({\mathbb {A}}\) is an algebra that is supernilpotent with respect to the 2-term higher commutator, and \({\mathbb {B}}\) is a subalgebra of \({\mathbb {A}}\), then \({\mathbb {B}}\) is representable as a retract of a finite subdirect power of \(\mathbb A\).

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Authors and Affiliations

  1. Department of Mathematics, University of Colorado, Boulder, CO, 80309-0395, USA

    Keith A. Kearnes

  2. Department of Higher Mathematics and Physics, Volgograd State Socio-Pedagogical University, Volgograd, Russia

    Alexander Rasstrigin

Authors
  1. Keith A. Kearnes
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  2. Alexander Rasstrigin
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Correspondence to Keith A. Kearnes.

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Presented by E. W. Kiss.

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This material is based upon work supported by the National Science Foundation Grant No. DMS 1500254.

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Kearnes, K.A., Rasstrigin, A. Representing subalgebras as retracts of finite subdirect powers. Algebra Univers. 81, 46 (2020). https://doi.org/10.1007/s00012-020-00675-5

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  • DOI: https://doi.org/10.1007/s00012-020-00675-5

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