Abstract
Let H be a finite involutary Hopfalgebra over the ring of integers Z. H is a separable Z-algebra iff H is dual to a finite groupring over Z. As a corollary one obtains a direct proof of a result by Tate-Oort: If H is of prime order p, then H is isomorphic to ZD or to its dual, where D=Z/pZ.
More generally some information is given about finite involutary Hopfalgebras over rings of algebraic integers.
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Literatur
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Schneider, HJ. Bemerkung zu einer Arbeit von Tate-Oort. Manuscripta Math 8, 319–322 (1973). https://doi.org/10.1007/BF01297665
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DOI: https://doi.org/10.1007/BF01297665