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Nontrivial solutions for homogeneous linear equations over some non-quotient hyperfields

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arxiv 2306.13232 v1 pith:WA3HXVVZ submitted 2023-06-22 math.RA

David Hobby , Jaiung Jun This is my paper · ORCID
classification math.RA
keywords hyperfieldsequationsnon-quotientclasshomogeneouslinearalwaysanswer
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We introduce a class of hyperfields which includes several constructions of non-quotient hyperfields. We then use it to partially answer a question posed by M. Baker and T. Zhang: Does a system of homogeneous linear equations with more unknowns than equations always have a nonzero solution? We also consider a class of hyperfields that was claimed in the literature to be non-quotient, and show that this is false.

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  1. 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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