Let H be a finite dimensional semisimple Hopf algebra over a field and A an H-module algebra. In this paper, we characterize any H-separable Galois extension of an Azumaya algebra. Assuming that A/AH is an H-separable...Let H be a finite dimensional semisimple Hopf algebra over a field and A an H-module algebra. In this paper, we characterize any H-separable Galois extension of an Azumaya algebra. Assuming that A/AH is an H-separable extension, we prove that A/AH is H-Galois and AH is Azumaya if and only if A#H is an Azumaya Z-algebra, where Z is the center of A#H(not necessarily C(A)H).展开更多
Let A be a finite-dimensional algebra over the real number field.We prove that the repetitive algebra A admits the dichotomy property of representation type,i.e.,A is either of discrete representation type or of stron...Let A be a finite-dimensional algebra over the real number field.We prove that the repetitive algebra A admits the dichotomy property of representation type,i.e.,A is either of discrete representation type or of strongly unbounded type.展开更多
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
Recently, we introduced the notion of a generalized derivation from a bimodule to a bimodule. In this paper, we give a more general notion based on commutators which covers generalized derivations as a special case. U...Recently, we introduced the notion of a generalized derivation from a bimodule to a bimodule. In this paper, we give a more general notion based on commutators which covers generalized derivations as a special case. Using it, we show that the separability of an algebra extension is characterized by generalized derivations.展开更多
基金The NSF (19771046) of China and Anhui Province Education Committee Fund (99jl0209).
文摘Let H be a finite dimensional semisimple Hopf algebra over a field and A an H-module algebra. In this paper, we characterize any H-separable Galois extension of an Azumaya algebra. Assuming that A/AH is an H-separable extension, we prove that A/AH is H-Galois and AH is Azumaya if and only if A#H is an Azumaya Z-algebra, where Z is the center of A#H(not necessarily C(A)H).
基金supported by the National Natural Science Foundation of China(Grant No.11961007)Science Technology Foundation of Guizhou Province(Grant Nos.[2018]1021,[2020]1Y405).
文摘Let A be a finite-dimensional algebra over the real number field.We prove that the repetitive algebra A admits the dichotomy property of representation type,i.e.,A is either of discrete representation type or of strongly unbounded type.
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.
文摘Recently, we introduced the notion of a generalized derivation from a bimodule to a bimodule. In this paper, we give a more general notion based on commutators which covers generalized derivations as a special case. Using it, we show that the separability of an algebra extension is characterized by generalized derivations.
