Geodesic
Prime z-Ideals of C(X) and Related Rings
Canadian mathematical bulletin, Tome 23 (1980) no. 4, pp. 437-443

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Let C(X) be the ring of continuous real-valued functions on a (completely regular) topological space X. The structure of the prime ideals and the prime z-ideals of C(X) has been the subject of much investigation (see e-g- [1], [3], [5]). One of the surprising facts about C(X) is that the sum of two prime ideals is again prime. 
Mason, Gordon. Prime z-Ideals of C(X) and Related Rings. Canadian mathematical bulletin, Tome 23 (1980) no. 4, pp. 437-443. doi: 10.4153/CMB-1980-064-3
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     author = {Mason, Gordon},
     title = {Prime {z-Ideals} of {C(X)} and {Related} {Rings}},
     journal = {Canadian mathematical bulletin},
     pages = {437--443},
     year = {1980},
     volume = {23},
     number = {4},
     doi = {10.4153/CMB-1980-064-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1980-064-3/}
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