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 language | English |
|---|---|
| Article number | 2150074 |
| Journal | Journal of Algebra and its Applications |
| Volume | 20 |
| Issue number | 5 |
| DOIs | |
| State | Published - May 2021 |
Keywords
- Kaplansky conjecture
- Noncommutative polynomials
- quaternion algebra
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