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 Characterizations of elements in prime radicals of skew polynomial rings and skew Laurent polynomial rings Bull. Korean Math. Soc. 2011 Vol. 48, No. 2, 277-290 https://doi.org/10.4134/BKMS.2011.48.2.277Printed March 1, 2011 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 $R$. Keywords : $\theta$-ideal, $\theta$-prime ideal, $\theta$-semiprime ideal, strongly $\theta$-nilpotent element, $\theta$-prime radical, prime radical, skew polynomial ring, skew Laurent polynomial ring MSC numbers : 16N40, 16N60, 16S36 Downloads: Full-text PDF