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- W2065241552 abstract "In [[6] Doi, Y. 1985. Algebras With Total Integrals. Comm. Algebra, 13: 2137–2159. [Web of Science ®] , [Google Scholar], Theorem 2.2] Doi gave a Hopf-algebraic proof of a generalization of Oberst's theorem on affine quotients of affine schemes. He considered a commutative Hopf algebra H over a field, coacting on a commutative H-comodule algebra A. If A coH denotes the subalgebra of coinvariant elements of A and β : A ⊗ A coH A → A ⊗ H the canonical map, he proved that the following are equivalent: a. AcoH ⊆ A is a faithfully flat Hopf Galois extension;b. the functor (−) coH : M H A → A coH -Mod is an equivalence;c. A is coflat as a right H-comodule and β is surjective. Schneider generalized this result in [[14] Schneider, H.-J. 1990. Principal Homogenous Spaces for Arbitrary Hopf Algebras. Israel J. Math., 72: 167–195. [Crossref], [Web of Science ®] , [Google Scholar], Theorem 1] to the non-commutative situation imposing as a condition the bijectivity of the antipode of the underlying Hopf algebra. Interpreting the functor of coinvariants as a Hom-functor, Menini and Zuccoli gave in [10] Menini, C. and Zuccoli, M. 1997. Equivalence Theorems and Hopf-Galois Extensions. J. Algebra, 194: 245–274. [Crossref], [Web of Science ®] , [Google Scholar] a module-theoretic presentation of parts of the theory. Refining the techniques involved we are able to generalize Schneiders result to H-comodule-algebras A for a Hopf algebra H (with bijective antipode) over a commutative ring R under fairly weak assumptions." @default.
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- W2065241552 date "2001-08-31" @default.
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- W2065241552 title "A-H-BIMODULES AND EQUIVALENCES" @default.
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