Bhatwadekar, S. M. ; Dutta, Amartya K. (1997) Kernel of locally nilpotent Rderivations of R[X,Y] Transactions of the American Mathematical Society, 349 (8). pp. 33033319. ISSN 00029947

PDF
 Publisher Version
307kB 
Official URL: http://www.ams.org/journals/tran/199734908/S0002...
Related URL: http://dx.doi.org/10.1090/S0002994797019466
Abstract
In this paper we study the kernel of a nonzero locally nilpotent Rderivation 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 Ralgebra 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 Rderivation 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 
Repository Staff Only: item control page