Quasi-k-normal ring

Abstract

In [4] Wei and Libin defined Quasi normal ring. In this paper we attempt to define Quasi-k-normal ring by using the action of k-potent element. A ring is called Quasi-k-normal ring if ae = 0 ⇒ eaRe = 0 for a ∈ N(R)and e ∈ K(R), where K(R) = {e ∈ R|ek = e}. Several analogous results give in [4] is defined here. we find here that a ring is quasi-k-normal if and only if eR(1 − ek−1)Re = 0 for each e ∈ K(R). Also we get a ring is quasi-k-normal ring if and only if Tn(R, R) is quasi-k-normal ring.