About weak $\pi$-rings

Abstract

As in \cite{J}, a ring is called a weak $\pi$-ring if every regular principal ideal is a finite product of prime ideals.In this paper, we establish some characterizations for weak $\pi$-rings. Also, we translate the properties weak $\pi$-ring and $(*)$-ring of $A\propto E$ in terms of a commutative ring $A$ and an $A$-module $E$.