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.
NR-clean ringπ-regular ringNGR-clean ringStrong NGR-clean ring
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