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

For any archimedean f-ring A with unit in which a A (1 - a) <= 0 for all a is an element of A, the following are shown to be equivalent: A is isomorphic to the l-ring 3L of all integer-valued continuous functions on some frame L. 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. For any family (a(n))(n is an element of w) in A there exists an l-ring homomorphism phi : C-z(Z(w)) -> A such that phi(p(n)) = a(n) for the product projections p :Z(w) -> Z. This provides an integer-valued counterpart to a familiar result concerning real-valued continuous functions.