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Let $p$ be a multilinear polynomial in several non-commuting variables withcoefficients 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 avector space. In this paper we settle the analogous conjecture for a quaternionalgebra.

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