Author/Authors :
Karimi Feizabadi، Abolghasem نويسنده Department of Mathematics,Islamic Azad University, Gorgan Branch,Gorgan,Iran , , Estaji، Ali Akbar نويسنده Faculty of Mathematics and Computer Sciences,Hakim Sabzevari University,Sabzevar,Iran , , Zarghani، Mohammad نويسنده Faculty of Mathematics and Computer Sciences, , Sabzevar, Iran.,Hakim Sabzevari University,Sabzevar,Iran ,
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 R to a frame L, is an f-ring, as a generalization of all functions from a set X into R. Also, we show that F(L) is isomorphic to a sub-ff-ring of R(L), the ring of real-valued continuous functions on L. Furthermore, for every frame L, there exists a Boolean frame BB such that F(L) is a sub-f-ring of F(B) ).
