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Affine algebras of Gelfand-Kirillov dimension one are PI

Published online by Cambridge University Press:  24 October 2008

L. W. Small ,
J. T. Stafford  and
R. B. Warfield Jr
L. W. Small
Affiliation:
Department of Mathematics, UCSD, La Jolla, CA 92093, U.S.A.
J. T. Stafford
Affiliation:
Department of Pure Mathematics, Leeds University, Leeds LS2 9JT, England
R. B. Warfield Jr
Affiliation:
Department of Mathematics, University of Washington, Seattle, W A 98195, U.S.A.
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Extract

The aim of this paper is to prove:

Theorem. Let R be an affine (finitely generated) algebra over a field k and of Gelfand-Kirillov dimension one. Then R satisfies a polynomial identity. Consequently, if N is the prime radical of R, then N is nilpotent and R/N is a finite module over its Noetherian centre.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 3 , May 1985 , pp. 407 - 414
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

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