Abstract
AbstractR. Paré and W. Schelter (1978) have extended the Cayley-Hamilton theorem by showing that for each n<1 there is an integer k such that all n x n matrices over any (possibly noncommutative) ring satisfy a monic polynomial of degree k. We give a lower bound for this degree, namely π(n), which is defined as the shortest possible length of a sequence with entries from {1, 2, …, n}.
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