A note on GK dimension of skew polynomial extensions
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- by James J. Zhang PDF
- Proc. Amer. Math. Soc. 125 (1997), 363-373 Request permission
Abstract:
Let $A$ be a finitely generated commutative domain over an algebraically closed field $k$, $\sigma$ an algebra endomorphism of $A$, and $\delta$ a $\sigma$-derivation of $A$. Then $\operatorname {GKdim}(A[x,\sigma ,\delta ])= \operatorname {GKdim}(A)+1$ if and only if $\sigma$ is locally algebraic in the sense that every finite dimensional subspace of $A$ is contained in a finite dimensional $\sigma$-stable subspace. Similarly, if $F$ is a finitely generated field over $k$, $\sigma$ a $k$-endomorphism of $F$, and $\delta$ a $\sigma$-derivation of $F$, then $\operatorname {GKdim} (F[x,\sigma ,\delta ])= \operatorname {GKdim}(F)+1$ if and only if $\sigma$ is an automorphism of finite order.References
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Additional Information
- James J. Zhang
- Affiliation: Department of Mathematics, Box 354350, University of Washington, Seattle, Washington 98195
- MR Author ID: 314509
- Email: zhang@math.washington.edu
- 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
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 363-373
- MSC (1991): Primary 16P90, 16S36
- DOI: https://doi.org/10.1090/S0002-9939-97-03602-2
- MathSciNet review: 1350966