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http://dx.doi.org/10.4134/BKMS.2011.48.2.277

CHARACTERIZATIONS OF ELEMENTS IN PRIME RADICALS OF SKEW POLYNOMIAL RINGS AND SKEW LAURENT POLYNOMIAL RINGS  

Cheon, Jeoung-Soo (Department of Mathematics Pusan National University)
Kim, Eun-Jeong (Department of Mathematics Pusan National University)
Lee, Chang-Ik (Department of Mathematics Pusan National University)
Shin, Yun-Ho (Department of Mathematics Pusan National University)
Publication Information
Bulletin of the Korean Mathematical Society / v.48, no.2, 2011 , pp. 277-290 More about this Journal
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 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;
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