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Title

On z◦ -ideals in C(X)

Authors 1, 1, 1

Affiliations

  1. Department of Mathematics, Chamran University, Ahvaz, Iran

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.

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Fundamenta Mathematicae
1999/160/1
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Pages:
15-25
Main language of publication
English
Received
1997-11-20
Accepted
1998-05-27
Published
1999
Exact and natural sciences