关于J-quasipolar环

摘要

The notion of J-quasipolar elements of rings was introduced by Cui Jian and Chen Jianlong in 2012.An element a in a ring R is J-quasipolar if there exists p 2=p∈comm2(a)satisfying a+p∈J(R),A ring called J-quasipolar ring if every element is J-quasipolar.It is shown that R is a J-quasiolar ring if and only if for R is a quasipolar ring and R is a strongly J#-clean ring.It is also proved that R is nil-quasipolar ring if and only if R is J-quasipolar ring and J(R)is nil.%2012 年,崔建和陈建龙提出了J-quasipolar元的概念.对于环R中的一个元素a,如果存在p 2=p∈comm2(a)使得a+p∈J(R),则称a为J-quasipolar 的.一个环称为J-quasipolar的,如果环中每一个元素都是J-quasipolar的.文章证明了一个环R是J-quasipolar环的充分必要条件是环R是quasipolar 环并且环R是强J #-clean环.同时也证明了一个环R是nil-quasipolar环当且仅当环R是J-quasipolar环并且J(R)是幂零的.