Finite Hyperfields of Order $n\leq 5$

Ziqi Liu

Finite Hyperfields of Order $n\leq 5$

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arxiv 2004.07241 v5 pith:6CWRF5KA submitted 2020-04-15 math.RA math.AC

Ziqi Liu This is my paper · ORCID

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In this paper, the author introduces the concept and basic properties of finite (commutative) hyperfields. Also, the author shows that, up to isomorphism, there are exactly 2 hyperfields of order 2; 5 hyperfields of order 3; 7 hyperfields of order 4; 27 hyperfields of order 5. Those hyperfields could be first hand materials for those who are doing relevant researches.

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On the borderline of fields and hyperfields, part II -- Enumeration and classification of the hyperfields of order 7
math.RA 2024-12 conditional novelty 6.0 of 10

There are exactly 277 seven-element hyperfields, all built on the cyclic multiplicative group of order six, and the paper classifies which of them arise as quotients of fields.

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