Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 12K99, 11T30

Retrieve articles in all journals with MSC (2010): 12K99, 11T30


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