Van den Essen's conjecture on the kernel of a derivation having a slice
Van den Essen's conjecture on the kernel of a derivation having a slice
复制标题
Van den Essen 关于具有切片的导数核的猜想
DOI：
10.1142/s0219498815400034
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Shigeru Kuroda
中科院分区：
文献类型：
--
作者：
根津智子;車谷典男;岩坂英巳ら;Shigeru Kuroda
多项式环的导子核的有限生成问题是希尔伯特第十四问题的一个特例。众所周知，如果导子是局部幂零的且有片，则答案是肯定的。货车登埃森（Van den Essen）（1995）猜想，存在具有切片的非局部幂零导子的反例。在本文中，我们肯定地解决了这个猜想。
The problem of finite generation of the kernel of a derivation of a polynomial ring is a special case of Hilbert's Fourteenth Problem. It is well known that the answer is affirmative if the derivation is locally nilpotent and having a slice. Van den Essen (1995) conjectured that there exists a counterexample for non-locally nilpotent derivations with a slice. In this paper, we solve this conjecture in the affirmative.