On the structure of hyperfields obtained as quotients of fields
Copyright policy )On the structure of hyperfields obtained as quotients of fields
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.
- Georgia Institute of Technology United States
- Shandong Women’s University China (People's Republic of)
- Mississippi School for Mathematics and Science United States
Mathematics - Number Theory, hyperfields, Rings and Algebras (math.RA), Hyperrings, FOS: Mathematics, Generalizations of fields, Mathematics - Rings and Algebras, Number Theory (math.NT), finite fields, Structure theory for finite fields and commutative rings (number-theoretic aspects)
Mathematics - Number Theory, hyperfields, Rings and Algebras (math.RA), Hyperrings, FOS: Mathematics, Generalizations of fields, Mathematics - Rings and Algebras, Number Theory (math.NT), finite fields, Structure theory for finite fields and commutative rings (number-theoretic aspects)
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