- Tytuł:
- On z◦ -ideals in C(X)
- Autorzy:
-
Azarpanah, F.
Karamzadeh, O.
Rezai Aliabad, A. - Powiązania:
- https://bibliotekanauki.pl/articles/1205250.pdf
- Data publikacji:
- 1999
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Opis:
- 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.
- Źródło:
-
Fundamenta Mathematicae; 1999, 160, 1; 15-25
0016-2736 - Pojawia się w:
- Fundamenta Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł