Commutative rings are studied which have the property that every ideal contained in the union of a collection of prime ideals is contained in one of the prime ideals of the collection. This property is shown to be equivalent to the condition that every prime ideal is the radical of a principal ideal. Received by the editors February 25, 1971. A MS 1970 subject classifications. Primary 13A15,13F05; Secondary 13E05, 13F10, 13A10.