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.