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)