Kernel of locally nilpotent derivations of
Authors:
S. M. Bhatwadekar and Amartya K. Dutta
Journal:
Trans. Amer. Math. Soc. 349 (1997), 33033319
MSC (1991):
Primary 13B10; Secondary 13A30
MathSciNet review:
1422595
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Abstract: In this paper we study the kernel of a nonzero locally nilpotent derivation of the polynomial ring over a noetherian integral domain containing a field of characteristic zero. We show that if is normal then the kernel has a graded algebra structure isomorphic to the symbolic Rees algebra of an unmixed ideal of height one in , and, conversely, the symbolic Rees algebra of any unmixed height one ideal in can be embedded in as the kernel of a locally nilpotent derivation of . We also give a necessary and sufficient criterion for the kernel to be a polynomial ring in general.
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Additional Information
S. M. Bhatwadekar
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay400 005, India
Email:
smb@tifrvax.tifr.res.in
Amartya K. Dutta
Affiliation:
Stat  Math Unit, Indian Statistical Institute, 203, B.T. Road, Calcutta700 035, India
Email:
amartya@isical.ernet.in
DOI:
http://dx.doi.org/10.1090/S0002994797019466
PII:
S 00029947(97)019466
Keywords:
Locally nilpotent derivations,
inert subrings,
symbolic Rees algebra
Received by editor(s):
January 11, 1996
Article copyright:
© Copyright 1997
American Mathematical Society
