z^(1/2)-Ideals and z°^(1/2)-Ideals in C(X)  

作　　者：F.AZARPANAH R.MOHAMADIAN 

机构地区：[1]Department of Mathematics,Chamran University,Ahvaz,Iran,Institute for Studies in Theoretical Physics and Mathematics,Tehran,Iran

出　　处：《Acta Mathematica Sinica,English Series》2007年第6期989-996,共8页数学学报（英文版）

基　　金：Institute for Studies in Theoretical Physics and Mathematics(IPM),Tehran

摘　　要：It is well known that every prime ideal minimal over a z-ideal is also a z-ideal. The converse is also well known in C（X）. Thus whenever I is an ideal in C（X）, then √I is a z-ideal if and only if I is, in which case √I = I. We show the same fact for z^-ideals and then it turns out that the sum of a primary ideal and a z-ideal （z^o-ideal） in C（X） which are not in a chain is a prime z-ideal （z^o-ideal）. We also show that every decomposable z-ideal （z^o-ideal） in C（X） is the intersection of a finite number of prime z-ideals （z^o-ideal）. Some counter-examples in general rings and some characterizations for the largest （smallest） z-ideal and z^o-ideal contained in （containing） an ideal are given.It is well known that every prime ideal minimal over a z-ideal is also a z-ideal. The converse is also well known in C（X）. Thus whenever I is an ideal in C（X）, then √I is a z-ideal if and only if I is, in which case √I = I. We show the same fact for z^-ideals and then it turns out that the sum of a primary ideal and a z-ideal （z^o-ideal） in C（X） which are not in a chain is a prime z-ideal （z^o-ideal）. We also show that every decomposable z-ideal （z^o-ideal） in C（X） is the intersection of a finite number of prime z-ideals （z^o-ideal）. Some counter-examples in general rings and some characterizations for the largest （smallest） z-ideal and z^o-ideal contained in （containing） an ideal are given.

关 键 词：√z-Ideals √z^o-Ideals quasi F-space almost P-space 

分 类 号：O153[理学—数学]