A note on triangular derivations of $\mathbf {k}[X_1,X_2,X_3,X_4]$
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- by Daniel Daigle and Gene Freudenburg PDF
- Proc. Amer. Math. Soc. 129 (2001), 657-662 Request permission
Abstract:
For a field $\mathbf {k}$ of characteristic zero, and for each integer $n\geq 4$, we construct a triangular derivation of $\mathbf {k} [X_1,X_2,X_3,X_4]$ whose ring of constants, though finitely generated over $\mathbf {k}$, cannot be generated by fewer than $n$ elements.References
- D. Daigle, G. Freudenburg, A counterexample to Hilbertβs Fourteenth Problem in dimension five, ppt 1999 (9 pages)
- M. Miyanishi, Normal affine subalgebras of a polynomial ring, in: Algebraic and Topological Theories β to the Memory of Dr. Takehiko Miyata, Kinokuniya, Tokyo (1985) 37-51
Additional Information
- Daniel Daigle
- Affiliation: Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada K1N 6N5
- Email: daniel@mathstat.uottawa.ca
- Gene Freudenburg
- Affiliation: Department of Mathematics, University of Southern Indiana, Evansville, Indiana 47712
- Email: freudenb@usi.edu
- Received by editor(s): March 25, 1999
- Received by editor(s) in revised form: May 12, 1999
- Published electronically: August 30, 2000
- Additional Notes: The first authorβs research was supported by NSERC Canada.
- Communicated by: Wolmer V. Vasconcelos
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 657-662
- MSC (2000): Primary 14R10; Secondary 14R20, 13N15
- DOI: https://doi.org/10.1090/S0002-9939-00-05558-1
- MathSciNet review: 1707514