Representation of real Riesz maps on a strong f-ring by prime elements of a frame

In classical topology, it is proved that for a topological space X, every bounded Riesz map (varphi :C (X) rightarrow {mathbb {R}}) is of the from ({hat{x}}) for a point (xin X). In this paper, our main purpose is to prove a version of this result by lattice-valued maps. A ring representation of the from (Arightarrow {mathbb {R}}) is constructed. This representation is denoted by (widetilde{p_c}) that is an onto f-ring homomorphism for every (pin Sigma L), where its index c, denotes a cozero lattice-valued map. Also, it is shown that for every Riesz map (phi :Arightarrow {mathbb {R}} ) and (cin F(A, L)) with specific properties, there exists (pin Sigma L) such that (phi =phi (1)widetilde{p_c}).