A note on GK dimension
of skew polynomial extensions
Author: James J. Zhang
Journal: Proc. Amer. Math. Soc. 125 (1997), 363-373
MSC (1991): Primary 16P90, 16S36
MathSciNet review: 1350966
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Abstract: Let be a finitely generated commutative domain over an algebraically closed field , an algebra endomorphism of , and a -derivation of . Then if and only if is locally algebraic in the sense that every finite dimensional subspace of is contained in a finite dimensional -stable subspace.
Similarly, if is a finitely generated field over , a -endomorphism of , and a -derivation of , then if and only if is an automorphism of finite order.
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James J. Zhang
Affiliation: Department of Mathematics, Box 354350, University of Washington, Seattle, Washington 98195
Keywords: Gelfand-Kirillov dimension, Polynomial extension, automorphism of algebra
Received by editor(s): June 19, 1995
Received by editor(s) in revised form: August 24, 1995
Additional Notes: This research was supported in part by the NSF
Communicated by: Ken Goodearl
Article copyright: © Copyright 1997 American Mathematical Society