Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Affine algebras of Gelfand-Kirillov dimension one are PI

L. W. Smalla1, J. T. Stafforda2 and R. B. Warfield Jra3

a1 Department of Mathematics, UCSD, La Jolla, CA 92093, U.S.A.

a2 Department of Pure Mathematics, Leeds University, Leeds LS2 9JT, England

a3 Department of Mathematics, University of Washington, Seattle, W A 98195, U.S.A.

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.

(Received August 13 1984)