Abstract. This note presents characterizations of the projective prime ideals in C{X) and of the hereditary and semihereditary rings of continuous functions.This note presents a characterization of the projective prime ideals in C(A), the ring of real-valued continuous functions on a completely regular Hausdorff space A. This characterization is then applied to obtain a characterization of the hereditary rings of continuous functions. The reader is referred to [5] and [2] for background. The referee has pointed out that the results in this paper can also be derived from the more general results appearing in [4].Lemma. Each projective prime ideal in C(X) is generated by an idempotent.
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