On the countably generated $z$-ideals of $C(X)$
HTML articles powered by AMS MathViewer
- by G. De Marco PDF
- Proc. Amer. Math. Soc. 31 (1972), 574-576 Request permission
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.References
- William E. Dietrich Jr., On the ideal structure of $C(X)$, Trans. Amer. Math. Soc. 152 (1970), 61–77. MR 265941, DOI 10.1090/S0002-9947-1970-0265941-2
- Leonard Gillman, Countably generated ideals in rings of continuous functions, Proc. Amer. Math. Soc. 11 (1960), 660–666. MR 156189, DOI 10.1090/S0002-9939-1960-0156189-X
- Leonard Gillman and Meyer Jerison, Rings of continuous functions, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0116199, DOI 10.1007/978-1-4615-7819-2
- Carl W. Kohls, A note on countably generated ideals in rings of continuous functions, Proc. Amer. Math. Soc. 12 (1961), 744–749. MR 143051, DOI 10.1090/S0002-9939-1961-0143051-2
- M. Mandelker, Round $z$-filters and round subsets of $\beta X$, Israel J. Math. 7 (1969), 1–8. MR 244951, DOI 10.1007/BF02771740
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 31 (1972), 574-576
- DOI: https://doi.org/10.1090/S0002-9939-1972-0288563-3
- MathSciNet review: 0288563