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arXiv · 1601.00748

On the flatness and the projectivity over Hopf subalgebras of Hopf algebras over discrete valuation rings

Nguyen Dai Duong·Phung Ho Hai·Nguyen Huy Hung
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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.

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Nguyen Dai Duong, Phung Ho Hai, Nguyen Huy Hung. 2016-01-05. On the flatness and the projectivity over Hopf subalgebras of Hopf algebras over discrete valuation rings. https://doi.org/10.1016/j.jalgebra.2017.01.015

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