Homological Dimension of Skew Group Rings and Crossed Products
Homological Dimension of Skew Group Rings and Crossed Products
复制标题
DOI：
10.1006/jabr.1994.1056
复制
发表时间：
1994-02
影响因子：
0.9
通讯作者：
Z. Yi
中科院分区：
文献类型：
--
作者：
Z. Yi
摘要本文研究了斜群环和交叉积的同调维数。如果R是右FBN和左相干的，并且G是有限的，那么用R的简单Artinian因子上的交叉积的形式给出了交叉积R * G具有有限右全局维的充分条件。给出了局部或半局部右noether环上有限群的斜群环R * G具有有限右整体维数的充分必要条件。然后，特别当R是交换诺etheran且G是有限时，我们得到了一个斜群环R * G具有有限整体维数的一些等价条件。利用Aljadeff的工作[E]。关于交叉积的Serre扩展定理，伦敦数学。Soc. 44(1991), 47-54]，这些结果推广到有限多环群。
Abstract In this paper we study the homological dimension of skew group rings and crossed products. A sufficient condition for R ∗ G , a crossed product, to have finite right global dimension is given, in terms of crossed products over simple Artinian factors of R if R is right FBN and left coherent and G is finite. Some necessary conditions and sufficient conditions for R ∗ G , a skew group ring of a finite group over a local or semilocal right Noetherian ring, to have finite right global dimension are also given. Then in particular if R is commutative Noetherian and G is finite, we obtain some equivalent conditions for R ∗ G , a skew group ring, to have finite global dimension. Using work of Aljadeff [E. Aljadeff, Serre′s extension theorem for crossed products, J. London Math. Soc. 44 (1991), 47-54], these results are extended to polycyclic-by-finite groups.