Some sufficient and necessary conditions are given for the equivalence between two crossed product actions of Hopf algebra H on the same linear category, and the Maschke theorem is generalized. Based on the result of ...Some sufficient and necessary conditions are given for the equivalence between two crossed product actions of Hopf algebra H on the same linear category, and the Maschke theorem is generalized. Based on the result of the crossed product in the classic Hopf algebra theory, first, let A be a k-linear category and H be a Hopf algebra, and the two crossed products A#_σH and A#＇_σH are isomorphic under some conditions. Then, let A#_σH be a crossed product category for a finite dimensional and semisimple Hopf algebra H. If V is a left A#σH-module and WC V is a submodule such that W has a complement as a left A-module, then W has a complement as a A#_σH-module.展开更多
The Chinese traditional aesthetic culture not only pay attention to the overall sense of He Xie （Harmony, 和谐）, and pay attention to a kind of artistic conception as Zi Wei （滋味）, Qi Yun （氣韵）, and YiJing （...The Chinese traditional aesthetic culture not only pay attention to the overall sense of He Xie （Harmony, 和谐）, and pay attention to a kind of artistic conception as Zi Wei （滋味）, Qi Yun （氣韵）, and YiJing （意境） as well. Mr. JI Xian-lin had tried to start from Zi Wei （滋味）, a new comprehension to open a new understanding on Chinese aesthetics. Hence, we embark from the Chinese aesthetic culture and its basic spirit, the humanistic connotation of Zi Wei （滋味）, which sounds with the basis, put forward it into a Music-Dance Spirit （乐舞精神） in Chinese art through this unique view, has made a new thinking to the Chinese traditional aesthetic artistic category system.展开更多
For a commtative ring R and an injective cogenerator E in the category of R-modules, we characterize QF rings, IF rings and semihereditary rings by using the properties of the dual modules with respect to E.
基金The National Natural Science Foundation of China(No.11371088)the Natural Science Foundation of Jiangsu Province(No.BK2012736)+1 种基金the Fundamental Research Funds for the Central Universitiesthe Research Innovation Program for College Graduates of Jiangsu Province(No.KYLX15_0109)
文摘Some sufficient and necessary conditions are given for the equivalence between two crossed product actions of Hopf algebra H on the same linear category, and the Maschke theorem is generalized. Based on the result of the crossed product in the classic Hopf algebra theory, first, let A be a k-linear category and H be a Hopf algebra, and the two crossed products A#_σH and A#＇_σH are isomorphic under some conditions. Then, let A#_σH be a crossed product category for a finite dimensional and semisimple Hopf algebra H. If V is a left A#σH-module and WC V is a submodule such that W has a complement as a left A-module, then W has a complement as a A#_σH-module.
文摘The Chinese traditional aesthetic culture not only pay attention to the overall sense of He Xie （Harmony, 和谐）, and pay attention to a kind of artistic conception as Zi Wei （滋味）, Qi Yun （氣韵）, and YiJing （意境） as well. Mr. JI Xian-lin had tried to start from Zi Wei （滋味）, a new comprehension to open a new understanding on Chinese aesthetics. Hence, we embark from the Chinese aesthetic culture and its basic spirit, the humanistic connotation of Zi Wei （滋味）, which sounds with the basis, put forward it into a Music-Dance Spirit （乐舞精神） in Chinese art through this unique view, has made a new thinking to the Chinese traditional aesthetic artistic category system.
基金Supported by National Natural Science Foundation of China (10001017)Scientific Research Foundation for Returned Overseas Chi
文摘For a commtative ring R and an injective cogenerator E in the category of R-modules, we characterize QF rings, IF rings and semihereditary rings by using the properties of the dual modules with respect to E.
