关于Qnilpotent环（英文）  

On Qnilpotent Rings

作　　者：郑振 陈焕艮[1] ZHENG Zhen;CHEN Huanyin(School of Mathematics,Hangzhou Normal University,Hangzhou 310036,China)

机构地区：[1]杭州师范大学理学院,浙江杭州310036

出　　处：《杭州师范大学学报（自然科学版）》2018年第4期424-429,共6页Journal of Hangzhou Normal University(Natural Science Edition)

基　　金：Supported by the Natural Science Foundation of Zhejiang Province(LY17A010018)

摘　　要：对于环R中的一个元素a,如果存在p^2=p∈comm^2(a)使得a+p∈R^(qnil),则称a为qnilpotent的,一个环称为qnilpotent的如果环中每一个元素都是qnilpotent的.文章证明了qnilpotent环是quasipolar的,若一个环R是qnilpotent的,则eRe也是qnilpotent的.同时给出了一些qnilpotent环与其相关的环之间的充分必要条件.证明了若R是一个局部环,则n×n阶上三角矩阵环是qnilpotent当且仅当R是唯一bleached的并且R/J(R)■Z_2.An element a of a ring R is qnilpotent if there exists p^2=p∈comm^2(a)such that a+p∈R^qnil,a ring called qnilpotent ring if every element is qnilpotent.This paper proves qnilpotent ring is quasipolar,and if a ring R is qnilpotent,then so is eRe.Several sufficient and necessary conditions between qnilpotent rings with related rings are obtained.It also proves that the n×n upper triangular matrix ring over a local ring R is qnilpotent if R is a uniquely bleached ring and R/J(R)Z≌2.

关 键 词：qnilpotent环 拟幂零元 quasipolar环 强nil-clean环 局部环 

分 类 号：O153.3[理学—数学]