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A Commutativity Theorem for Division Rings

Published online by Cambridge University Press:  20 November 2018

Anthony Richoux
Anthony Richoux*
Affiliation:
Department of Mathematics North Carolina State University Raleigh, North Carolina27607
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Abstract

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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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 2 , 01 June 1980 , pp. 241 - 243
Copyright
Copyright © Canadian Mathematical Society 1980

References

1. Herstein, I. N., The Structure of a Certain Class of Rings, Amer. J. Math. 75 (1953), 866-871.Google Scholar
2. Chacron, M., On a Theorem of Herstein, Canada J. Math. 21 (1969), 1348-1353.Google Scholar