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A NOTE ON GROUP IDENTITIES IN DIVISION RINGS

Published online by Cambridge University Press:  09 November 2004

M. A. Chebotar  and
P.-H. Lee
M. A. Chebotar
Affiliation:
Department of Mechanics and Mathematics, Tula State University, Tula, Russia ([email protected])
P.-H. Lee
Affiliation:
Department of Mathematics, National Taiwan University, Taipei, Taiwan, Republic of China ([email protected])
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Abstract

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Let $D$ be a division ring whose group of units satisfies a non-trivial group identity $w$. Let $\alpha$ be the sum of positive degrees of indeterminates occurring in $w$. If the centre of $D$ contains more than $3\alpha$ elements, then $D$ is commutative.

AMS 2000 Mathematics subject classification: Primary 16R50. Secondary 16K20

Keywords

division ringgroup of unitsgroup identitypolynomial identity
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 47 , Issue 3 , October 2004 , pp. 557 - 560
Copyright
Copyright © Edinburgh Mathematical Society 2004