%0 Journal Article %T The ring of real-valued functions on a frame %J Categories and General Algebraic Structures with Applications %I Shahid Beheshti University %Z 2345-5853 %A Karimi Feizabadi, Abolghasem %A Estaji, Ali Akbar %A Zarghani, Mohammad %D 2016 %\ 07/01/2016 %V 5 %N 1 %P 85-102 %! The ring of real-valued functions on a frame %K frame %K $f$-ring %K Ring of real-valued functions %R %X In this paper, we define and study the notion of the real-valued functions on a frame $L$. We show that $F(L) $, consisting of all frame homomorphisms from the power set of $\mathbb{R}$ to a frame $ L$, is an $f$-ring, as a generalization of all functions from a set $X$ into $\mathbb R$. Also, we show that $F(L) $ is isomorphic to a sub-$f$-ring of $\mathcal{R}(L)$, the ring of real-valued continuous functions on $L$. Furthermore, for every frame $L$, there exists a Boolean frame $B$ such that $F(L)$ is a sub-$f$-ring of $ F(B)$. %U https://cgasa.sbu.ac.ir/article_14685_3fb4a5800764dc102f3cbb565968e45d.pdf