中文摘要：

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.

英文摘要：

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.