In this paper,we study the stability of the orthogonal equation,which is closely related to the results by W.Fechner and J.Sikorska in 2010.There are some differences that we consider the target space with theβ-homog...In this paper,we study the stability of the orthogonal equation,which is closely related to the results by W.Fechner and J.Sikorska in 2010.There are some differences that we consider the target space with theβ-homogeneous norm and quasi-norm.Overcoming theβ-homogeneous norm and quasi-norm bottlenecks,we get some new results.展开更多
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 c...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.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.1197149312071491)the Fundamental Research Funds for the Central Universities(Grant No.2021qntd21)。
文摘In this paper,we study the stability of the orthogonal equation,which is closely related to the results by W.Fechner and J.Sikorska in 2010.There are some differences that we consider the target space with theβ-homogeneous norm and quasi-norm.Overcoming theβ-homogeneous norm and quasi-norm bottlenecks,we get some new results.
基金Institute for Studies in Theoretical Physics and Mathematics(IPM),Tehran
文摘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.
