Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58535120160701The ring of real-valued functions on a frame8510214685ENAbolghasem Karimi FeizabadiDepartment of Mathematics, Gorgan Branch, Islamic Azad University, Gorgan, Iran.Ali Akbar EstajiFaculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran.Mohammad ZarghaniFaculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran.Journal Article20151227In 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)$.https://cgasa.sbu.ac.ir/article_14685_3fb4a5800764dc102f3cbb565968e45d.pdf