π-Clean and strongly π-clean rings

In this paper, π-regular (resp. strongly π-regular) and idempotent elements in a ring is used to define π-clean (resp. strongly π-clean) rings. A ring is called π-clean (resp. strongly π-clean) if each of its elements is the sum of a π-regular (resp. strongly π-regular) and an idempotent element. The purpose of this research is to give some results on π-clean and strongly π-clean rings and study π-clean and strongly π-clean group rings. Also, this paper is involved with investigating F2C2 as a social group and measuring influence a member of it's rather than others.