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A note on the kernel
of a locally nilpotent derivation


Author: Gene Freudenburg
Journal: Proc. Amer. Math. Soc. 124 (1996), 27-29
MSC (1991): Primary 13B25; Secondary 14L30
DOI: https://doi.org/10.1090/S0002-9939-96-03003-1
MathSciNet review: 1285990
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Abstract | References | Similar Articles | Additional Information

Abstract: This note concerns locally nilpotent derivations $D$ of the polynomial ring $\mathbf C[X_1,\dots, X_n]$. It is shown that if $D$ annihilates a polynomial in two variables, then $D$ annihilates a variable.


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

  • 1 R. Rentschler, Opérations du groupe additif sur le plan affine, C.R. Acad. Sci. Paris Sér. A 267 (1968), 384--387. MR 38:1093
  • 2 I. R. Shafarevich, Fundamentals of algebraic geometry, Nauka, Moscow, 1988 (Vols. 1 and 2). MR 90g:14001;MR 90g:14002
  • 3 D. Snow, Unipotent actions on affine space, Topological Methods in Algebraic Transformation Groups, Birkhäuser, Boston, 1989. MR 91f:14048

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Additional Information

Gene Freudenburg
Affiliation: Department of Mathematical Sciences, Ball State University, Muncie, Indiana 47306
Address at time of publication: Department of Mathematics, University of Southern Indiana, Evansville, Indiana 47712

DOI: https://doi.org/10.1090/S0002-9939-96-03003-1
Received by editor(s): June 6, 1994
Received by editor(s) in revised form: July 15, 1994
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1996 American Mathematical Society

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