【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。更多还原

【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.更多还原