Geodesic
On $z^\circ$-ideals in $C(X)$
Fundamenta Mathematicae, Tome 160 (1999) no. 1, pp. 15-25.

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An ideal I in a commutative ring R is called a z°-ideal if I consists of zero divisors and for each a ∈ I the intersection of all minimal prime ideals containing a is contained in I. We characterize topological spaces X for which z-ideals and z°-ideals coincide in , or equivalently, the sum of any two ideals consisting entirely of zero divisors consists entirely of zero divisors. Basically disconnected spaces, extremally disconnected and P-spaces are characterized in terms of z°-ideals. Finally, we construct two topological almost P-spaces X and Y which are not P-spaces and such that in every prime z°-ideal is either a minimal prime ideal or a maximal ideal and in C(Y) there exists a prime z°-ideal which is neither a minimal prime ideal nor a maximal ideal.
DOI : 10.4064/fm_1999_160_1_1_15_25

F. Azarpanah 1 ; O. A. S. Karamzadeh 1 ; A. Rezai Aliabad 1

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F. Azarpanah; O. A. S. Karamzadeh; A. Rezai Aliabad. On $z^\circ$-ideals in $C(X)$. Fundamenta Mathematicae, Tome 160 (1999) no. 1, pp. 15-25. doi : 10.4064/fm_1999_160_1_1_15_25. http://geodesic.mathdoc.fr/articles/10.4064/fm_1999_160_1_1_15_25/

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