Uniquely strongly clean triangular matrix rings  

唯一强clean三角矩阵环(英文)

作　　者：崔建[1] 陈建龙[1] 

机构地区：[1]东南大学数学系,南京211189

出　　处：《Journal of Southeast University(English Edition)》2011年第4期463-465,共3页东南大学学报（英文版）

基　　金：The National Natural Science Foundation of China(No.10971024);the Specialized Research Fund for the Doctoral Program of Higher Education(No.200802860024);the Natural Science Foundation of Jiangsu Province(No.BK2010393)

摘　　要：An element a of a ring R is called uniquely strongly clean if it is the sum of an idempotent and a unit that commute, and in addition, this expression is unique. R is called uniquely strongly clean if every element of R is uniquely strongly clean. The uniquely strong cleanness of the triangular matrix ring is studied. Let R be a local ring. It is shown that any n × n upper triangular matrix ring over R is uniquely strongly clean if and only if R is uniquely bleached and R/J（R） ≈Z2.称一个环R中的元素a是唯一强clean的,如果a可以唯一地表示成幂等元和可逆元的和且二者可交换.称环R是唯一强clean的,如果R中每一个元素都是唯一强clean元.研究了n×n阶三角矩阵环的唯一强clean性.设R为局部环,证明了环R上的任意n×n阶上三角矩阵环是唯一强clean的当且仅当R是唯一bleached的且R/J(R)Z2.

关 键 词：uniquely strongly clean ring uniquely bleached local ring triangular matrix ring 

分 类 号：O153.3[理学—数学]