the ring of real-valued functions on a frame
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abstract
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)$.
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Journal title:
categories and general algebraic structures with applicationجلد ۵، شماره ۱، صفحات ۸۵-۱۰۲
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