Q-clean环的结构及其应用（英文）  

The structure of Q-clean ring and its application

作　　者：孙晓青[1] 刘霞 花秀娟[1] Sun Xiaoqing;Liu Xia;Hua Xiujuan(School of Science,Xi'an University of Technology,Xi'an 710054,China)

机构地区：[1]西安理工大学理学院

出　　处：《纯粹数学与应用数学》2019年第2期215-222,共8页Pure and Applied Mathematics

基　　金：国家自然科学基金(61806162);西安理工大学校基金(2015CX009)

摘　　要：定义了Q-clean环,并对它做了深入的研究,得到了Q-clean环的很多特性.特别的,证明了在2可逆的Q-clean环中,每个元素都可以表示为一个拟可逆元和一个幂等元的和.还得到了Q-clean环的一个充分条件,即如果环R的每个元素可以写成x=xux, u∈Rq^-1,则R是Q-clean环.最后,证明了Q-clean环的理想仍然是Q-clean的.The notions of Q-clean elements in a ring and Q-clean ring are defined. Some basic properties of Q-clean rings are obtained. In particular, it is shown that every element in a Q-clean ring with 2 invertible is a sum of a quasi-invertible element and a square root of 1. Let R be a ring in which every element x ∈ R, x = xux where u ∈ Rq^-1. Then R is Q-clean. Furthermore, we prove that the ideals of a Q-clean ring are also Q-clean.

关 键 词：拟可逆 Q-clean环 理想 

分 类 号：O153.3[理学—数学]