Characterizing f-rings
Peter D. Colville · Glasgow Mathematical Journal · 1975
Birkhoff and Pierce [2] introduced the class f-rings—those lattice-ordered rings R which satisfy the additional condition that if a, b, and c are positive elements of R and if a ∧ b = 0, then ac ∧ b = 0 = ca ∧ b. They showed that f-rings may be characterized as lattice-ordered rings which are subdirect products of totally-ordered rings.