Let R be a ring and let H be a.subgroup of a finite group G.We consider the weak global dimension,cotorsion dimension and weak Gorenstein global dimension of the skew group ring R^σ G and its coefficient ring R.Under...Let R be a ring and let H be a.subgroup of a finite group G.We consider the weak global dimension,cotorsion dimension and weak Gorenstein global dimension of the skew group ring R^σ G and its coefficient ring R.Under the assumption that R^σ G is a,separable extension over R^σ H,it is shown that R^σ G and R^σ H share the same homological dimensions.Several known results are then obtained as corollaries.Moreover,we investigate the relationships between the homological dimensions of Ra G and the homological dimensions of a commutative ring R,using the trivial R^σ G-module.展开更多
基金supported by the Scientific Research Foundation of Hunan Provincial Education Department(no.18C0997).
文摘Let R be a ring and let H be a.subgroup of a finite group G.We consider the weak global dimension,cotorsion dimension and weak Gorenstein global dimension of the skew group ring R^σ G and its coefficient ring R.Under the assumption that R^σ G is a,separable extension over R^σ H,it is shown that R^σ G and R^σ H share the same homological dimensions.Several known results are then obtained as corollaries.Moreover,we investigate the relationships between the homological dimensions of Ra G and the homological dimensions of a commutative ring R,using the trivial R^σ G-module.
