Characterizations of elements in prime radicals of skew polynomial rings and skew Laurent polynomial rings
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We show that the θ-prime radical of a ring R is the set of all strongly θ-nilpotent elements in R, where θ is an automorphism of R. We observe some conditions under which the θ-prime radical of R coincides with the prime radical of R. Moreover we characterize elements in prime radicals of skew Laurent polynomial rings, studying (θ, θ^-1)-(semi)primeness of ideals of R.
Abstract
We show that the θ-prime radical of a ring R is the set of all strongly θ-nilpotent elements in R, where θ is an automorphism of R. We observe some conditions under which the θ-prime radical of R coincides with the prime radical of R. Moreover we characterize elements in prime radicals of skew Laurent polynomial rings, studying (θ, θ^-1)-(semi)primeness of ideals of R.
참고문헌 (5)
- S. S. Bedi, "Jacobson radical of skew polynomial rings and skew group rings", Israel J. Math, 35(4), pp.327~338 (1980)
- J. Lambek, "Lectures on Rings and Modules" (1976), Chelsea Publishing Co
- T. Y. Lam, "Primeness, semiprimeness and prime radical of Ore extensions", Comm. Algebra, 25(8), pp.2459~2506 (1997)
- K. R. Pearson, "A skew polynomial ring over a Jacobson ring need not be a Jacobson ring", Comm. Algebra, 5(8), pp.783~794 (1977)
- K. R. Pearson, "Skew polynomials and Jacobson rings", Proc. London Math. Soc. (3), 42(3), pp.559~576 (1981)