A note on lattices of \(z\)-ideals of \(f\)-rings. (Q302287)

The author proves that if \(A\) is some \(f\)-ring (with bounded inversion), then the lattice of \(z\)-ideals of \(A\) is a normal coherent Yosida frame. Consequently, the author obtains the main purpose: the ring \(C(X)\) of real valued continuous functions defined on completely regular space is an \(f\)-ring with bounded inversion then the lattice of \(z\)-ideals of \(C(X)\) is a normal coherent Yosida frame.