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.2011.48.2.277
Printed 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
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