The kernel of a derivation
The kernel of a derivation
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推导的核心
DOI：
10.1016/0022-4049(93)90159-q
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发表时间：
1993
影响因子：
0.8
通讯作者：
H. Derksen
中科院分区：
文献类型：
--
作者：
H. Derksen
设K是特征为0的域。Nagata和Nowicki证明了K [X1，.，Xn]上导子的核在Kifn ≤3上是有限型的.本文构造了一个核不是有限型的32元多项式环的导子。进一步证明了对于有限超越度的域扩张LoverK，L中代数闭的中间域是L的K-导子的核。
LetKbe a field of characteristic 0. Nagata and Nowicki have shown that the kernel of a derivation onK[X1,…,Xn] is of finite type overKifn≤3. We construct a derivation of a polynomial ring in 32 variables which kernel is not of finite type overK. Furthermore we show that for every field extensionLoverKof finite transcendence degree, every intermediate field which is algebraically closed inLis the kernel of aK-derivation ofL.