TY - JOUR
ID - 14685
TI - The ring of real-valued functions on a frame
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Karimi Feizabadi, Abolghasem
AU - Estaji, Ali Akbar
AU - Zarghani, Mohammad
AD - Department of Mathematics, Gorgan Branch, Islamic Azad University, Gorgan, Iran.
AD - Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran.
Y1 - 2016
PY - 2016
VL - 5
IS - 1
SP - 85
EP - 102
KW - frame
KW - $f$-ring
KW - Ring of real-valued functions
DO -
N2 - 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)$.
UR - https://cgasa.sbu.ac.ir/article_14685.html
L1 - https://cgasa.sbu.ac.ir/article_14685_3fb4a5800764dc102f3cbb565968e45d.pdf
ER -