Prime z-Ideals of C(X) and Related Rings

Gordon Mason

doi:10.4153/CMB-1980-064-3

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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.

References

1. Gillman, L. and Jerison, M., Rings of Continuous Functions, Van Nostrand, New York, 1960.Google Scholar

2. Hochster, M., Prime ideal structure in commutative rings, Trans. Amer. Math Soc. 149 (1969), 43-60.Google Scholar

3. Kohls, C. W., Prime ideals in rings of continuous functions, Illinois J. Math 2 (1958), 505-536.Google Scholar

4. Mason, G., z-ideals and prime ideals, J. Algebra 26 (1973) 280-297.Google Scholar

5. Rudd, D., On two sum theorems for ideals of C(X), Michigan Math. J. 17 (1970) 139-141.Google Scholar

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