NGR-clean环OA
NGR-clean Ring
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 se-veral expansions of(strong…查看全部>>
王志强;吴俊
安徽师范大学数学与统计学院,安徽芜湖,241003安徽师范大学数学与统计学院,安徽芜湖,241003
数学
NR-clean环π-正则环NGR-clean环强NGR-clean环
NR-clean ringπ-regular ringNGR-clean ringStrong NGR-clean ring
《宿州学院学报》 2024 (3)
9-14,21,7
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