Projective ideals in rings of continuous functions

An ideal in a ring A is said to be projective provided it is a projective -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 ^-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 2-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.