.z .Ideals and z.... .Ideals in C(X)

It is well known that every prime ideal minimal over a z.ideal is also a z.ideal. The converse is also well known in C(X). Thus whenever I is an ideal in C(X), then I.. is a z.ideal if and only if I is, in which case I..=I. We show the same fact for z ..ideals and then it turns out that the sum of a primary ideal and a z.ideal (z ..ideal) in C(X) which are not in a chain is a prime z.ideal (z ..ideal). We also show that every decomposable z.ideal (z ..ideal) in C(X) is the intersection of a finite number of prime z.ideals (z ..ideal). Some counter.examples in general rings and some characterizations for the largest (smallest) z.ideal and z ..ideal contained in (containing) an ideal are given.