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

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 projectivit...

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Bibliographic Details
Published in:arXiv.org 2017-01
Main Authors: Nguyen Dai Duong, Phung Ho Hai, Nguyen, Huy Hung
Format: Article
Language:English
Subjects:
Algebra
Flatness
Integrals
Modules
Rings (mathematics)
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1601.00748