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.
@article{bwmeta1.element.bwnjournal-article-fmv160i1p15bwm,
author = {F. Azarpanah and O. Karamzadeh and A. Rezai Aliabad},
title = {On z* -ideals in C(X)},
journal = {Fundamenta Mathematicae},
volume = {159},
year = {1999},
pages = {15-25},
zbl = {0991.54014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv160i1p15bwm}
}
Azarpanah, F.; Karamzadeh, O.; Rezai Aliabad, A. On z◦ -ideals in C(X). Fundamenta Mathematicae, Tome 159 (1999) pp. 15-25. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv160i1p15bwm/
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