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A note on triangular derivations of $\mathbf{k}[X_1,X_2,X_3,X_4]$


Authors: Daniel Daigle and Gene Freudenburg
Journal: Proc. Amer. Math. Soc. 129 (2001), 657-662
MSC (2000): Primary 14R10; Secondary 14R20, 13N15
Published electronically: August 30, 2000
MathSciNet review: 1707514
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. D. Daigle, G. Freudenburg, A counterexample to Hilbert's Fourteenth Problem in dimension five, ppt 1999 (9 pages)
  • 2. M. Miyanishi, Normal affine subalgebras of a polynomial ring, in: Algebraic and Topological Theories - to the Memory of Dr. Takehiko Miyata, Kinokuniya, Tokyo (1985) 37-51 CMP 91:10

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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

DOI: https://doi.org/10.1090/S0002-9939-00-05558-1
Keywords: Derivations, Hilbert fourteenth problem, additive group actions, invariants
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 author’s research was supported by NSERC Canada.
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 2000 American Mathematical Society