  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.

Rings and Algebras