Representation of real Riesz maps on a strong <Emphasis Type="Italic">f</Emphasis>-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 \(x\in X\). In this paper, our main purpose is to prove a version of this result by lattice-valued maps. A ring representation of the from \(A\rightarrow {\mathbb {R}}\) is constructed. This representation is denoted by \(\widetilde{p_c}\) that is an onto f-ring homomorphism for every \(p\in \Sigma L\), where its index c, denotes a cozero lattice-valued map. Also, it is shown that for every Riesz map \(\phi :A\rightarrow {\mathbb {R}} \) and \(c\in F(A, L)\) with specific properties, there exists \(p\in \Sigma L\) such that \(\phi =\phi (1)\widetilde{p_c}\).