Jeoung Soo Cheon, Eun Jeong Kim, Chang Ik Lee, and Yun Ho Shin Pusan National University, Pusan National University, Pusan National University, Pusan National University

Abstract : We show that the $\theta$-prime radical of a ring $R$ is the set of all strongly $\theta$-nilpotent elements in $R$, where $\theta$ is an automorphism of $R$. We observe some conditions under which the $\theta$-prime radical of $R$ coincides with the prime radical of $R$. Moreover we characterize elements in prime radicals of skew Laurent polynomial rings, studying $(\theta,\theta^{-1})$-(semi)primeness of ideals of $R$.