f-ring

Summary

An f-ring is a lattice-ordered ring in which multiplying by a nonnegative element keeps disjoint elements disjoint. The notion was introduced by Birkhoff and Pierce. Rings of continuous real functions with the pointwise order, and products of totally ordered rings, are f-rings. Every f-ring is a subdirect product of totally ordered rings, so f-rings behave in many ways like rings of real functions.