Kernel of locally nilpotent R-derivations of R[X,Y]

Bhatwadekar, S. M. ; Dutta, Amartya K. (1997) Kernel of locally nilpotent R-derivations of R[X,Y] Transactions of the American Mathematical Society, 349 (8). pp. 3303-3319. ISSN 0002-9947

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In this paper we study the kernel of a non-zero locally nilpotent R-derivation of the polynomial ring R[ X, Y ] over a noetherian integral domain R containing a field of characteristic zero. We show that if R is normal then the kernel has a graded R-algebra structure isomorphic to the symbolic Rees algebra of an unmixed ideal of height one in R, and, conversely, the symbolic Rees algebra of any unmixed height one ideal in R can be embedded in R[ X, Y ] as the kernel of a locally nilpotent R-derivation of R[ X, Y ]. We also give a necessary and sufficient criterion for the kernel to be a polynomial ring in general.

Item Type:Article
Source:Copyright of this article belongs to American Mathematical Society.
ID Code:3203
Deposited On:11 Oct 2010 09:59
Last Modified:16 May 2016 14:03

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