English

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}
}
R2 v1 2026-06-28T11:12:25.611Z