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

Publisher： Cambridge University Press

E-ISSN： 1755-1633|49|1|85-90

ISSN： 0004-9727

Source： Bulletin of the Australian Mathematical Society, Vol.49, Iss.1, 1994-02, pp. : 85-90

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Abstract

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−1 x−1 ax)q(x) K for all x D ﹨ {0} where q(x) is a positive integer depending on x. Then a K.

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