The images of noncommutative polynomials evaluated on the quaternion algebra

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Abstract

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

Original languageEnglish
Article number2150074
JournalJournal of Algebra and its Applications
Volume20
Issue number5
DOIs
StatePublished - May 2021

Keywords

  • Kaplansky conjecture
  • Noncommutative polynomials
  • quaternion algebra

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