Abstract:We determine all isomorphism classes of hyperfields of a given finite order which can be obtained as quotients of finite fields of sufficiently large order. Using this result, we determine which hyperfields of order at most 4 are quotients of fields. The main ingredients in the proof are the Weil bounds from number theory and a result from Ramsey theory.

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中文翻译：

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关于作为场商获得的超场的结构

摘要：我们确定给定有限阶超场的所有同构类，这些同构类可以作为足够大阶的有限域的商获得。使用此结果，我们确定最多4个阶的超场是场的商。证明中的主要成分是数论的Weil边界和Ramsey理论的结果。

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