2023/06/22 by David Hobby, Hobby, David, Jaiung Jun +1 · 1 citation
Computer Science · Mathematics · #15A06 (secondary) #16Y20 (primary) #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #FOS: Mathematics #Polynomial and algebraic computation #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2306.13232
openalex publication_date 2023/06/22 · openalex created_date 2023/06/27 · openalex updated_date 2026/07/28
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.