Prime ideals in differential operator rings and crossed products of infinite groups
Prime ideals in differential operator rings and crossed products of infinite groups
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微分算子环中的素理想和无限群的叉积
DOI：
10.1016/0021-8693(87)90022-6
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发表时间：
1987
影响因子：
0.9
通讯作者：
W. Chin
中科院分区：
文献类型：
--
作者：
W. Chin
利用Martindale商环的一个版本，研究了两种情况下环r的扩展中的素数理想。如果g是R的一组自同构，我们就形成了交叉积R * g。如果g是R的导数的李代数，我们就得到了用R * g表示的扭曲微分算子环（有时称为“扭曲”的smash积r# t u (g)）。我们得到幂零群的交叉积和可解李代数的微分算子环的不可比较的类似物。在交叉积的情况下，推广了DS Passman和M. Lorenz关于无限循环群的不可比性结果（也由G. Bergman证明）。
We use a version of the Martindale ring of quotients to study prime ideals in extensions of a ringR corresponding to two cases. IfG is a group of automorphisms ofR we form the crossed product R∗ G. If g is a Lie algebra of derivations of R we have the twisted differential operator ring, denoted byR∗ g (sometimes known as the “twisted” smash product R# t u (g)). We obtain analogues of Incomparability for crossed products of nilpotent groups, and differential operator rings of solvable Lie algebras. In the case of crossed products, the incomparability result of DS Passman and M. Lorenz for the infinite cyclic group (also proved by G. Bergman) is generalized.