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A bialgebra that admits a Hopf-Galois extension is a Hopf algebra
Authors:Peter Schauenburg
Institution:Department of Mathematics University of Southern California, Los Angeles, California 90089
Abstract:Let $k$ be a commutative ring. Assume that $H$ is a $k$-bialgebra, and $A$ is an $H$-Galois extension of its coinvariant subalgebra $B$. Provided $A$ is faithfully flat over $k$, we show that $H$ is necessarily a Hopf algebra.

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