On Multilinear Polynomials In Four Variables Evaluated On Matrices
classification
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keywords
evaluatedfourmatricesmultilinearvariablesalgebraicallycharacteristicclosed
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Let $K$ be an algebraically closed field of characteristic $0$ and let $M_n(K)$, $n \ge 3$, be the matrix ring over $K$. We will show that the image of any multilinear polynomial in four variables evaluated on $M_n(K)$ contains all matrices of trace $0$.
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