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arXiv · 1912.11496

On the structure of hyperfields obtained as quotients of fields

Matthew Baker·Tong Jin
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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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Matthew Baker, Tong Jin. 2019-12-24. On the structure of hyperfields obtained as quotients of fields. https://doi.org/10.1090/proc%2F15207

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