On Zg-Clean Rings

Let r be an associative ring with unity. an element x ∈ r is called zg-clean if x = e + r, where e is an idempotent and r is a zg-regular element in r. a ring r is called zg-clean if every element of r is zg-clean. in this paper, we show that in an abelian zgregular ring r, the nil(r) is a two-sided ideal of r and r/ nil(r) is g-regular. furthermore,we characterize zg-clean rings. also, this paper is involved with investigating f2c2 as a social group and measuring influence a member of it’s rather than others.