Kernel of locally nilpotent -derivations

of

Authors:
S. M. Bhatwadekar and Amartya K. Dutta

Journal:
Trans. Amer. Math. Soc. **349** (1997), 3303-3319

MSC (1991):
Primary 13B10; Secondary 13A30

DOI:
https://doi.org/10.1090/S0002-9947-97-01946-6

MathSciNet review:
1422595

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we study the kernel of a non-zero 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, Bombay-400 005, India

Email:
smb@tifrvax.tifr.res.in

**Amartya K. Dutta**

Affiliation:
Stat - Math Unit, Indian Statistical Institute, 203, B.T. Road, Calcutta-700 035, India

Email:
amartya@isical.ernet.in

DOI:
https://doi.org/10.1090/S0002-9947-97-01946-6

Keywords:
Locally nilpotent derivations,
inert subrings,
symbolic Rees algebra

Received by editor(s):
January 11, 1996

Article copyright:
© Copyright 1997
American Mathematical Society