Normal bases for Hopf-Galois algebras

Abstract:

Let $H$ be a Hopf algebra over a commutative ring $R$ such that $H$ is a finitely generated, projective module over $R$, let $A$ be a right $H$-comodule algebra, and let $B$ be the subalgebra of $H$-coinvariant elements of $A$. If $A$ is a Galois extension of $B$ and $B$ is a local subalgebra of the center of $A$, then $A$ is a cleft right $H$-comodule algebra or, equivalently, there is a normal basis for $A$ over $B$.