Algebraic properties of rings of continuous functions

Volume 149 / 1996

M. A. Mulero Fundamenta Mathematicae 149 (1996), 55-66 DOI: 10.4064/fm-149-1-55-66


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.


  • M. A. Mulero

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