Moody's induction theorem
Moody's induction theorem
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穆迪归纳定理
DOI：
10.1215/ijm/1255989000
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发表时间：
1988
影响因子：
0.6
通讯作者：
A. Weiss
中科院分区：
文献类型：
--
作者：
G. Cliff;A. Weiss
我们的目的是给出约翰·穆迪[1]最近著名的归纳法定理的一个证明，这个证明简单明了，或多或少是自包含的。设I是有限群生成的交换元，S，I是左Nother环S与F的交叉积。放手(S I‘)表示所有有限生成的S，F-模范畴的Grothendieck群。对于F的任意子群F，都有一个映射GO(S，F)GO(S，F)，这是通过将一个S的F-模M的类[M]发送到诱导模的类[S，F(R)S，F-M]而给出的。
Our purpose is to give a proof of the recent remarkable induction theorem of John Moody [1], a proof that is straightforward and more or less self contained. Let I" be a finitely generated abelian by finite group, and let S, I" be a crossed product of a left noetherian ring S with F. Let Go(S I’) denote the Grothendieck group of the category of all finitely generated S, F-modules. For any subgroup F of F, there is a map Go(S, F) Go(S, F) given by sending the class [M] of an S, F-module M to the class [S, F (R)s, F M] of the induced module.