交换环中理想的w-整闭包

w-integral closure of ideals in commutative rings

R是一个交换环,利用交换环中w-星型算子,本文给出了R中任意理想I的w-整闭包的定义,推广了整闭包的定义.本文首先证明了交换环R中w-整闭包的保持性质;其次,证明了交换环R中理想I的w-整闭包的局部化的四个等价性质;最后,给出了元素r属于GV-无挠理想I的w-整闭包的充分必要条件.

Let R be a commutative ring. This paper defines the w-integral closure of ideals with w- operation,which generalizes integral closure of ideals. Firstly,the persistent property of the w-integral closure inR is proved; Moreover,four equivalent properties of the w-integral closure under localization are shown. Finally,the sufficient and necessary conditions are given that r belongs to the w- integral clousure of I.