Geodesic
Algebraic properties of rings of continuous functions
Fundamenta Mathematicae, Tome 149 (1996) no. 1, pp. 55-66.

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This paper is devoted to the study of algebraic properties of rings of continuous functions. Our aim is to show that these rings, even if they are highly non-noetherian, have properties quite similar to the elementary properties of noetherian rings: we give going-up and going-down theorems, a characterization of z-ideals and of primary ideals having as radical a maximal ideal and a flatness criterion which is entirely analogous to the one for modules over principal ideal domains.
DOI : 10.4064/fm-149-1-55-66
Keywords: rings of continuous functions, going-up and going-down theorems, z-ideals, primary ideals, flat modules

M. A. Mulero 1

1 
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M. A. Mulero. Algebraic properties of rings of continuous functions. Fundamenta Mathematicae, Tome 149 (1996) no. 1, pp. 55-66. doi : 10.4064/fm-149-1-55-66. http://geodesic.mathdoc.fr/articles/10.4064/fm-149-1-55-66/

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