NGR-clean环
NGR-clean Ring
王志强 1吴俊1
作者信息
- 1. 安徽师范大学数学与统计学院,安徽芜湖,241003
- 折叠
摘要
若环R中的任意元素都能表示成一个(强)π-正则元和一个幂零元之和,则称环R是(强)NGR-clean环.研究给出(强)NGR-clean环的一些基本性质,证明了若I是环R的诣零理想,则R是NGR-clean环当且仅当R/I是NGR-clean环.此外,还研究了(强)NGR-clean环与一些环类之间的联系以及(强)NGR-clean环的几类扩张.
Abstract
If any element of a ring R can be represented as the sum of a(strong)π-regular element and a nilpotent element,then the ring R is said to be a(strong)NGR-clean ring.Some basic properties of the(strong)NGR-clean rings are given.It proves that if I is a nil ideal of a ring R,then the ring R is a NGR-clean ring if and only if R/I is a NGR-clean ring.In addition,the connection between(strong)NGR-clean rings and some ring classes,and se-veral expansions of(strong)NGR-clean rings are also studied.
关键词
NR-clean环/π-正则环/NGR-clean环/强NGR-clean环Key words
NR-clean ring/π-regular ring/NGR-clean ring/Strong NGR-clean ring引用本文复制引用
出版年
2024
国家科技期刊平台
NSTL
万方数据