NGR-clean环  

NGR-clean Ring

作　　者：王志强 吴俊 WANG Zhiqiang;WU Jun(College of Mathematics and Statistics,Anhui Normal University,Wuhu 241003,China)

机构地区：[1]安徽师范大学数学与统计学院,安徽芜湖241003

出　　处：《宿州学院学报》2024年第3期9-14,21,共7页Journal of Suzhou University

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。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 several 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 

分 类 号：O153.3[理学—数学]