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Skew fields with a non-trivial generalised power central rational identity

Published online by Cambridge University Press:  17 April 2009

Katsuo Chiba
Katsuo Chiba
Affiliation:
Niihama National College of Technology, 7-1 Yagumo-Cho, Niihama 792, Japan
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Abstract

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Let D be a skew field with uncountable centre K. The main result in the present paper is as follows: If D satisfies a non-trivial generalised power central rational identity, then D is finite dimensional over K. As a corollary we obtain the following result. Let a be an element of D such that (a−1x−1ax)q(x) ∈ K for all x ∈ D ﹨ {0} where q(x) is a positive integer depending on x. Then a ∈ K.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 49 , Issue 1 , February 1994 , pp. 85 - 90
Copyright
Copyright © Australian Mathematical Society 1994

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