Pure ideals in commutative reduced Gelfand rings with unity (Q1117271)

In this paper, pure ideals in the class of all commutative reduced Gelfand rings with unity are classified. Then as an application, we prove that any pure ideal in the ring C(X) of all continuous real valued functions over a completely regular Hausdorff space has the form \(\cap_{x\in K}0_ x \), where K is a closed subset of the Stone- Čech compactification \(\beta\) X of X.