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.

翻译：在文章中,我们引入了一条测算仪的流量多数值, 并用它从通俗代数角度研究无处零流动。 我们使用Hilbert's Nullstelllensatz, 在无处零流动和双向流动之间建立了关系。 对于平面图来说, 这提供了无处零流动和双向双向流动之间的关系。 它也提供了很有说服力的证据, 证明每个无桥三角图都有一个无处零四流。