RS rings and their applications

In this paper, a ring $R$ is said to be an RS ring if every regular element is strongly regular. It is shown that the concept of RS rings is a generalization of those of abelian rings and nilpotent-closed rings. Various properties of RS rings are investigated. As applications, we study the properties of rings related to RS properties. Some well-known results on regular elements and $\pi$-regular elements in commutative rings are generalized.