On sπ-Weakly Regular Rings

A ring R is said to be right(left) sπ-weakly regular if for each a ∈ R and a positive integer n, a n ∈ a n R a n 2 R (a n ∈ R a n 2 R a n ). In this paper, we continue to study sπ-weakly regular rings due to R. D. Mahmood and A. M. Abdul-Jabbar (8). We first consider properties and basic extensions of sπ-weakly regular rings, and we give the connection of s π-weakly regular, semi π-regular and π-biregular rings.