Rings of quotients of the ring consisting of ordered field valued continuous functions with countable range

For a zero-dimensional topological space X and totally ordered field F with interval topology, Cc(X, F) denotes the ring consisting of field-valued continuous functions countable range on X. This article aims to study investigate rings quotients Cc(X,F). Qc(X,F) (resp. qc(X,F)), maximal classical) Cc(X,F) as modified analogue Q(X) q(X)), C(X) are characterized. It is proved that Qc(S), subring S Cc(X,F), Qc(X, if only every dense ideal in has cozero-set Also, coincidence investigated. We show qc(X,F)=Cc(X, set non-units zero-divisors coincide almost CPF-space. Finally, it shown fixed cofinite Cc(X) Hom(Mcp) = Cc(Xp) for p ?