理想簇和根理想

The Variety of Ideal and Radical Ideal

关于环的理想的根有两种定义,一种是所有包含I的极大理想的交,另一种是所有包含I的素理想交,本文主要研究后者定义的一些性质,以及和理想簇V(I)(所有包含I的素理想的集合)的关系.

there are two definitions about radical of an ideal I of a ring R,one definition of the radical is defined as the intersection of all maximum ideals of R containing I,the other is defined as the intersection of all prime ideals of R containing I.In this article we discuss mainly the latter definition.