On the structure of hyperfields obtained as quotients of fields
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- by Matthew Baker and Tong Jin PDF
- Proc. Amer. Math. Soc. 149 (2021), 63-70 Request permission
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.References
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Additional Information
- Matthew Baker
- Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
- MR Author ID: 638188
- Email: mbaker@math.gatech.edu
- Tong Jin
- Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
- Address at time of publication: Taishan College, Shandong University, Jinan, People’s Republic of China
- Email: tjinmath@outlook.com
- Received by editor(s): February 14, 2020
- Received by editor(s) in revised form: April 29, 2020
- Published electronically: October 20, 2020
- Communicated by: Romyar T. Sharifi
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 149 (2021), 63-70
- MSC (2010): Primary 12K99; Secondary 11T30
- DOI: https://doi.org/10.1090/proc/15207
- MathSciNet review: 4172586