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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the countably generated $ z$-ideals of $ C(X)$


Author: G. De Marco
Journal: Proc. Amer. Math. Soc. 31 (1972), 574-576
DOI: https://doi.org/10.1090/S0002-9939-1972-0288563-3
MathSciNet review: 0288563
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Abstract | References | Additional Information

Abstract: A necessary and sufficient condition for the countable generation of certain $ z$-ideals of $ C(X)$ is given. In particular, for $ X$ compact, the countably generated $ z$-ideals of $ C(X)$ are the sets of all functions which vanish on a neighborhood of some zero-set of $ X$. Any finitely generated semiprime ideal of $ C(X)$ is generated by an idempotent.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0288563-3
Keywords: $ z$-ideal, countably generated $ z$-ideal, semiprime ideal
Article copyright: © Copyright 1972 American Mathematical Society