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

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

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
@article{10_4153_CMB_1980_064_3,
     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/}
}
TY  - JOUR
AU  - Mason, Gordon
TI  - Prime z-Ideals of C(X) and Related Rings
JO  - Canadian mathematical bulletin
PY  - 1980
SP  - 437
EP  - 443
VL  - 23
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1980-064-3/
DO  - 10.4153/CMB-1980-064-3
ID  - 10_4153_CMB_1980_064_3
ER  - 
%0 Journal Article
%A Mason, Gordon
%T Prime z-Ideals of C(X) and Related Rings
%J Canadian mathematical bulletin
%D 1980
%P 437-443
%V 23
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1980-064-3/
%R 10.4153/CMB-1980-064-3
%F 10_4153_CMB_1980_064_3

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

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

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

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

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

Cité par Sources :