Extensions of Quasipolar Rings

Abstract

In this paper we define and study quasipolar general rings (with or without identity) and extend many of the basic results to the wider class. We obtain some new characterizations of quasipolar and strongly $\pi$-regular elements by using quasipolar general rings. We see that quasipolar general rings lies between strongly $\pi$-regular and strongly clean general rings. Consequently, we prove that $R$ is pseudopolar if and only if $R$ is strongly $\pi$-rad clean and quasipolar.