Nontrivial solutions for homogeneous linear equations over some non-quotient hyperfields
Rings and Algebras
2023-06-26 v1
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.
Keywords
Cite
@article{arxiv.2306.13232,
title = {Nontrivial solutions for homogeneous linear equations over some non-quotient hyperfields},
author = {David Hobby and Jaiung Jun},
journal= {arXiv preprint arXiv:2306.13232},
year = {2023}
}