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

Hobby, David; Jun, Jaiung

doi:10.1090/proc/16727

Nontrivial solutions for homogeneous linear equations over some non-quotient hyperfields
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by David Hobby and Jaiung Jun

Proc. Amer. Math. Soc.

DOI: https://doi.org/10.1090/proc/16727

Published electronically: March 20, 2024

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Abstract:

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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