An example of a simple derivation in two variables
An example of a simple derivation in two variables
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DOI：
10.4064/cm113-1-3
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发表时间：
2008
影响因子：
0.4
通讯作者：
A. Nowicki
中科院分区：
文献类型：
--
作者：
A. Nowicki
设k为特征为零的场。证明了多项式环k（x;y）的导数D =@ =@x + (y s + px)(@=@y)，其中s 2,06 p2 k是简单的。1. 介绍。在整篇论文中，k是一个特征为零的域。假设d是可交换k代数R的一个导数。如果R除了0和R之外没有d不变理想，我们说d是简单的。简单的导数对于构造非域的简单非交换环是有用的。众所周知（(2)），如果R（t;d）是矿石
Let k be a field of characteristic zero. We prove that the derivation D = @=@x + (y s + px)(@=@y), where s 2, 06 p2 k, of the polynomial ring k(x;y) is simple. 1. Introduction. Throughout the paper k is a field of characteristic zero. Assume that d is a derivation of a commutative k-algebra R. We say that d is simple if R has no d-invariant ideals other than 0 and R. Simple derivations are useful for constructions of simple noncommutative rings which are not fields. It is well known ((2)) that if R(t;d) is the Ore