Geodesic
A Commutativity Theorem for Division Rings
Canadian mathematical bulletin, Tome 23 (1980) no. 2, pp. 241-243

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Let D be a division ring with center Z. Suppose for all xεD, there exists a monic polynomial, fx(t), with integer coefficients such that fx(x)εZ. Then D is commutative. 
Richoux, Anthony. A Commutativity Theorem for Division Rings. Canadian mathematical bulletin, Tome 23 (1980) no. 2, pp. 241-243. doi: 10.4153/CMB-1980-033-7
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[1] 1. Herstein, I. N., The Structure of a Certain Class of Rings, Amer. J. Math. 75 (1953), 866-871. Google Scholar

[2] 2. Chacron, M., On a Theorem of Herstein, Canada J. Math. 21 (1969), 1348-1353. Google Scholar

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