In this article we introduce the flow polynomial of a digraph and use it to
study nowhere-zero flows from a commutative algebraic perspective. Using
Hilbert's Nullstellensatz, we establish a relation between nowhere-zero flows
and dual flows. For planar graphs this gives a relation between nowhere-zero
flows and flows of their planar duals. It also yields an appealing proof that
every bridgeless triangulated graph has a nowhere-zero four-flow