进一步将二阶Morita Context环上的部分性质推广到了三阶Morita Context环上.设O=[R C E A S F B D T]是三阶Morita Context环,证明了:1)O是π-正则的(或半Clean的、Exchange的、Potent的、GM-环)当且仅当R、S和T也是该类环;2)O是左Morp...进一步将二阶Morita Context环上的部分性质推广到了三阶Morita Context环上.设O=[R C E A S F B D T]是三阶Morita Context环,证明了:1)O是π-正则的(或半Clean的、Exchange的、Potent的、GM-环)当且仅当R、S和T也是该类环;2)O是左Morphic环当且仅当R、S、T是左Morphic的,且A=B=C=D=E=F=0.展开更多
Let H be a finite-dimensional weak Hopf algebra and A a left H-module algebra with its invariant subalgebra A^H.We prove that the smash product A#H is an A-ring with a grouplike character, and give a criterion for A#H...Let H be a finite-dimensional weak Hopf algebra and A a left H-module algebra with its invariant subalgebra A^H.We prove that the smash product A#H is an A-ring with a grouplike character, and give a criterion for A#H to be Frobenius over A. Using the theory of A-rings, we mainly construct a Morita context 〈A^H,A#H,A,A,τ,μ〉 connecting the smash product A#H and the invariant subalgebra A^H , which generalizes the corresponding results obtained by Cohen, Fischman and Montgomery.展开更多
文摘进一步将二阶Morita Context环上的部分性质推广到了三阶Morita Context环上.设O=[R C E A S F B D T]是三阶Morita Context环,证明了:1)O是π-正则的(或半Clean的、Exchange的、Potent的、GM-环)当且仅当R、S和T也是该类环;2)O是左Morphic环当且仅当R、S、T是左Morphic的,且A=B=C=D=E=F=0.
基金Supported by the NSF of China(1097104910971052)+1 种基金the NSF of Hebei Province(A2008000135A2009000253)
文摘Let H be a finite-dimensional weak Hopf algebra and A a left H-module algebra with its invariant subalgebra A^H.We prove that the smash product A#H is an A-ring with a grouplike character, and give a criterion for A#H to be Frobenius over A. Using the theory of A-rings, we mainly construct a Morita context 〈A^H,A#H,A,A,τ,μ〉 connecting the smash product A#H and the invariant subalgebra A^H , which generalizes the corresponding results obtained by Cohen, Fischman and Montgomery.
