Representing subalgebras as retracts of finite subdirect powers

Keith A. Kearnes; Alexander Rasstrigin

Representing subalgebras as retracts of finite subdirect powers

Group Theory 2020-05-07 v1 Logic Rings and Algebras

Authors: Keith A. Kearnes , Alexander Rasstrigin

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 $\mathbb A$ .

Keywords

universal algebra subalgebra retract finite subdirect power supernilpotent higher commutator

Cite

@article{arxiv.2005.02461,
  title  = {Representing subalgebras as retracts of finite subdirect powers},
  author = {Keith A. Kearnes and Alexander Rasstrigin},
  journal= {arXiv preprint arXiv:2005.02461},
  year   = {2020}
}

Comments

13 pages. Keywords: abelian, formation, higher commutator, pseudovariety, supernilpotent, two term condition, unary algebra

Representing subalgebras as retracts of finite subdirect powers

Abstract

Keywords

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