%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