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

Title & Authors
CHARACTERIZATIONS OF ELEMENTS IN PRIME RADICALS OF SKEW POLYNOMIAL RINGS AND SKEW LAURENT POLYNOMIAL RINGS
Cheon, Jeoung-Soo; Kim, Eun-Jeong; Lee, Chang-Ik; Shin, Yun-Ho;

Abstract
We show that the $\small{{\theta}}$-prime radical of a ring R is the set of all strongly $\small{{\theta}}$-nilpotent elements in R, where $\small{{\theta}}$ is an automorphism of R. We observe some conditions under which the $\small{{\theta}}$-prime radical of coincides with the prime radical of R. Moreover we characterize elements in prime radicals of skew Laurent polynomial rings, studying ($\small{{\theta}}$, $\small{{\theta}^{-1}}$)-(semi)primeness of ideals of R.
Keywords
$\small{{\theta}}$-ideal;$\small{{\theta}}$-prime ideal;$\small{{\theta}}$-semiprime ideal;strongly $\small{{\theta}}$-nilpotent element;$\small{{\theta}}$-prime radical;prime radical;skew polynomial ring;skew Laurent polynomial ring;
Language
English
Cited by
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STRUCTURE OF ZERO-DIVISORS IN SKEW POWER SERIES RINGS,;;;

대한수학회지, 2015. vol.52. 4, pp.663-683
1.
Radicals of skew polynomial rings and skew Laurent polynomial rings, Journal of Algebra, 2011, 331, 1, 428
2.
STRUCTURE OF ZERO-DIVISORS IN SKEW POWER SERIES RINGS, Journal of the Korean Mathematical Society, 2015, 52, 4, 663
3.
On σ-nil ideals of bounded index of σ-nilpotence, Journal of Algebra, 2012, 371, 492
4.
Radicals in skew polynomial and skew Laurent polynomial rings, Journal of Pure and Applied Algebra, 2014, 218, 10, 1916
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