On the flatness and the projectivity over Hopf subalgebras of Hopf algebras over discrete valuation rings
arXiv:1601.00748 · doi:10.1016/j.jalgebra.2017.01.015
Abstract
We study the flatness and the projectivity of Hopf algebras, defined over a Dedekind ring, over their Hopf subalgebras. We give a criterion for the faithful flatness and use it to show the faithful flatness of an arbitrary flat Hopf algebra upon its finite normal Hopf subalgebra. For the projectivity of a projective Hopf algebras we need some finiteness condition in terms of the module of integral. In particular we show the the module of integral has rank one.
Final version, to appear in Journal of Algebra