Let CΨ(X) be the ideal of functions with pseudocompact
support and let kX be the set of all points in υX having compact neighborhoods. We show that
CΨ(X) is pure if and only if βX−kX is a round subset of βX, CΨ(X) is a projective C(X)-module if and
only if CΨ(X) is pure and kX is paracompact. We also show that if
CΨ(X) is
pure, then for each f∈CΨ(X) the ideal (f) is a projective (flat) C(X)-module if and only if kX is basically disconnected (F′-space).