The images of non-commutative polynomials evaluated on the Quaternion algebra

Sergey Malev

The images of non-commutative polynomials evaluated on the Quaternion algebra

Rings and Algebras 2019-06-13 v1

Authors: Sergey Malev

Abstract

Let $p$ be a multilinear polynomial in several non-commuting variables with coefficients in an arbitrary field $K$ . Kaplansky conjectured that for any $n$ , the image of $p$ evaluated on the set $M_n(K)$ of $n$ by $n$ matrices is a vector space. In this paper we settle the analogous conjecture for a quaternion algebra.

Keywords

non-commutative polynomial quaternion algebra multilinear polynomial kaplansky conjecture matrix algebra vector space

Cite

@article{arxiv.1906.04973,
  title  = {The images of non-commutative polynomials evaluated on the Quaternion algebra},
  author = {Sergey Malev},
  journal= {arXiv preprint arXiv:1906.04973},
  year   = {2019}
}

Related papers

View all related →

Algebraic Geometry · Mathematics

The images of non-commutative polynomials evaluated on $2\times 2$ matrices over an arbitrary field