A necessary and sufficient condition for the countable generation of certain z-ideals of C(X) is given. In particular, for A'compact, the countably generated z-ideals of CYJQare 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. © 1972 American Mathematical Society.
On the countably generated z-ideals of C(X)
DE MARCO, GIUSEPPE
1972
Abstract
A necessary and sufficient condition for the countable generation of certain z-ideals of C(X) is given. In particular, for A'compact, the countably generated z-ideals of CYJQare 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. © 1972 American Mathematical Society.
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