# On z◦ -ideals in C(X)

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

Fundamenta Mathematicae (1999)

- Volume: 160, Issue: 1, page 15-25
- ISSN: 0016-2736

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topAzarpanah, F., Karamzadeh, O., and Rezai Aliabad, A.. "On z◦ -ideals in C(X)." Fundamenta Mathematicae 160.1 (1999): 15-25. <http://eudml.org/doc/212377>.

@article{Azarpanah1999,

abstract = {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.},

author = {Azarpanah, F., Karamzadeh, O., Rezai Aliabad, A.},

journal = {Fundamenta Mathematicae},

language = {eng},

number = {1},

pages = {15-25},

title = {On z◦ -ideals in C(X)},

url = {http://eudml.org/doc/212377},

volume = {160},

year = {1999},

}

TY - JOUR

AU - Azarpanah, F.

AU - Karamzadeh, O.

AU - Rezai Aliabad, A.

TI - On z◦ -ideals in C(X)

JO - Fundamenta Mathematicae

PY - 1999

VL - 160

IS - 1

SP - 15

EP - 25

AB - 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.

LA - eng

UR - http://eudml.org/doc/212377

ER -

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