摘要
本文研究了余挠对在有限群分次和非分次情况下的联系.利用分次理论以及相对同调,我们首先研究了R是任意环G是有限群的情况下,余挠对在R-模范畴以及斜群环S=R*G-模范畴之间的关系;然后我们研究了R-gr范畴中刚性余挠对的等价刻画,同时给出了余挠对在R-gr范畴与R-模范畴之间的关系,其中R是G分次环,群G是有限群且|G|^(-1)∈R.
In this paper,we study the relation of cotorsion pairs between the graded and ungraded cases.By using the graded theory and the relative homological algebra,we first consider the relationship of cotorsion pairs in R-mod and S = R＊ G-mod when R is any ring and G is a finite group.Then we study rigid cotorsion pairs in R-gr and consider the relationship of cotorsion pairs between R-gr and R-mod when R is a ring graded by a finite group G with ｜G｜^-1 ∈ R.
出处
《数学杂志》
CSCD
北大核心
2015年第2期227-236,共10页
Journal of Mathematics
基金
Supported by by the School Foundation of Yangzhou University(2012CXJ004)
NSFC(11326065)
关键词
余挠对
有限群分次环
cotorsion pair
finite group graded ring
