On the structure of hyperfields obtained as quotients of fields
Authors:
Matthew Baker and Tong Jin
Journal:
Proc. Amer. Math. Soc. 149 (2021), 63-70
MSC (2010):
Primary 12K99; Secondary 11T30
DOI:
https://doi.org/10.1090/proc/15207
Published electronically:
October 20, 2020
Full-text PDF
Abstract | References | Similar Articles | Additional Information
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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Additional Information
Matthew Baker
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
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
DOI:
https://doi.org/10.1090/proc/15207
Keywords:
Hyperfields,
finite fields.
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
Article copyright:
© Copyright 2020
American Mathematical Society
