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Kernel of locally nilpotent $R$-derivations of $R[X,Y]$.
- Source :
-
Transactions of the American Mathematical Society . Aug1997, Vol. 349 Issue 8, p3303-3319. 17p. - Publication Year :
- 1997
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *POLYNOMIAL rings
*ALGEBRA
Subjects
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 349
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 9494938
- Full Text :
- https://doi.org/10.1090/S0002-9947-97-01946-6