An ideal in a ring Λ is
said to be projective provided it is a projective Λ-module. This paper is
concerned with the problem of topologically characterizing projectivity within the
class of ideals of a ring of continuous functions. Since there are projective
and nonprojective ideals having the same z-filter, the possibility of such a
characterization appears remote. However, such a characterization is shown to
exist for the projective z-ideals. Moreover, a relationship between projective
z-ideals and arbitrary projective ideals is exhibited and used to show that,
in some cases, every projective ideal is module isomorphic to a projective
z-ideal.
