Geodesic
Intersections of Primary Ideals in Rings of Continuous Functions
Canadian journal of mathematics, Tome 24 (1972) no. 3, pp. 502-519

Voir la notice de l'article provenant de la source Cambridge University Press

Let C be the ring of all real valued continuous functions on a completely regular topological space. This paper is an investigation of the ideals of C that are intersections of prime or of primary ideals.C. W. Kohls has analyzed the prime ideals of C in [3 ; 4] and the primary ideals of C in [5]. He showed that these ideals are absolutely convex. (An ideal I of C is called absolutely convex if |f| ≦ |g| and g ∈ I imply that f ∈ I.) It follows that any intersection of prime or of primary ideals is absolutely convex. We consider here the problem of finding a necessary and sufficient condition for an absolutely convex ideal I of C to be an intersection of prime ideals and the problem of finding a necessary and sufficient condition for I to be an intersection of primary ideals. 
Williams, R. Douglas. Intersections of Primary Ideals in Rings of Continuous Functions. Canadian journal of mathematics, Tome 24 (1972) no. 3, pp. 502-519. doi: 10.4153/CJM-1972-043-8
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[5] 5. Kohls, C. W., Primary ideals in rings of continuous functions, Amer. Math. Monthly 71 (1964), 980–984. Google Scholar

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