free ideals and real ideals of the ring of frame maps from p(r) to a frame

Let f p(l) (f∗p(l)) be the f-rings of all (bounded) frame maps from p(r) to a frame l. fp∞(l) is the family of all f∈f p(l) such that ↑f(−1/n,1/n) is compact for any n∈n and the subring f p k(l) is the family of all f∈f p(l) such that coz(f) is compact. we introduce and study the concept of real ideals in fp(l) and f∗p(l). we show that every maximal ideal of f∗p(l) is real, and also we study the relation between the conditions ''l is compact and ''every maximal ideal of f p(l) is real''. we prove that for every nonzero real riesz map φ:f p(l)→r, there is an element p in σl such that φ=p coz˜ if l is a zero-dimensional frame for which b(l) is a sub-σ-frame of l and every maximal ideal of f p(l) is real. we show that f p∞(l) is equal to the intersection of all free maximal ideals of f∗p(l) if b(l) is a sub-σ-frame of a zero-dimensional frame l and also, f p k(l) is equal to the intersection of all free ideals f p(l) (resp., f∗p(l)) if l is a zero-dimensional frame. also, we study free ideals and fixed ideals of f p∞(l) and f p k(l).