Countable composition closedness and integer-valued continuous functions in pointfree topology

For any archimedean f-ring A with unit in which a ^ (1 - α ) ≤ 0 for all α ∈ A, the following are shown to be equivalent: 1. A is isomorphic to the l-ring 3L of all integer-valued continuous functions on some frame L. 2. A is a homomorphic image of the l-ring C_Z(X) of all integer-valued continuous functions, in the usual sense, on some topological space X. 3. For any family (α_n)n∈w in A there exists an l-ring homomorphism Φ: Z^ (Z^ w)→ A such that Φ(p_n) = αn for the product projections pn : Z^w → Z. This provides an integer-valued counterpart to a familiar result concerning real-valued continuous functions.