Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
MathSciNet review: 1285990
Full-text PDF Free Access

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 Rudolf Rentschler, Opérations du groupe additif sur le plan affine, C. R. Acad. Sci. Paris Sér. A-B 267 (1968), A384–A387 (French). MR 0232770 (38 #1093)
  • 2 I. R. Shafarevich, Osnovy algebraicheskoi geometrii. Tom 1, 2nd ed., “Nauka”, Moscow, 1988 (Russian). Algebraicheskie mnogoobraziya v proektivnom prostranstve. [Algebraic varieties in projective space]. MR 969372 (90g:14001)
    I. R. Shafarevich, Osnovy algebraicheskoi geometrii. Tom 2, 2nd ed., “Nauka”, Moscow, 1988 (Russian). Skhemy. Kompleksnye mnogoobraziya. [Schemes. Complex varieties]. MR 979764 (90g:14002)
  • 3 Dennis M. Snow, Unipotent actions on affine space, Topological methods in algebraic transformation groups (New Brunswick, NJ, 1988) Progr. Math., vol. 80, Birkhäuser Boston, Boston, MA, 1989, pp. 165–176. MR 1040863 (91f:14048)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 13B25, 14L30

Retrieve articles in all journals with MSC (1991): 13B25, 14L30


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: http://dx.doi.org/10.1090/S0002-9939-96-03003-1
PII: S 0002-9939(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