关于惟一强π rad clean元
On uniquely strongly π rad clean elements

环R中的元素a称为是惟一强π rad clean的，如果存在惟一的幂等元e∈R使得a-e∈u(R),ea=ae且ean∈J(R),其中n是某个正整数。如果环中的每一个元素都是惟一强π rad clean元，那么环称为是惟一强π rad clean环。文中给出了惟一强π rad clean元和阿贝尔的惟一强π rad clean环的一些等价刻画。
An element a of a ring R is said to be uniquely strongly π rad clean if there exists a unique idempotent e∈R such that a-e∈u(R)，ea=ae and ean∈J(R) for some positive integer n. If every element is uniquely strongly π rad clean, then R is called the uniquely strongly π rad clean ring. In this paper, some characterizations of uniquely strongly π rad clean elements and abelian uniquely strongly π rad clean rings are given