Radicals of Ore Extension of Skew Armendariz Rings |
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Authors: | A R Nasr-Isfahani |
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Institution: | 1. Department of Mathematics, University of Isfahan, Isfahan, Iran;2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Irannasr_a@sci.ui.ac.ir |
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Abstract: | Let R be a ring with an endomorphism α and an α-derivation δ. In this article, for a skew-Armendariz ring R we study some properties of skew polynomial ring Rx; α, δ]. In particular, among other results, we show that for an (α, δ)-compatible skew-Armendariz ring R, γ(Rx; α, δ]) = γ(R)x; α, δ] = Ni?*(R)x; α, δ], where γ is a radical in the class of radicals which includes the Wedderburn, lower nil, Levitzky, and upper nil radicals. We also show that several properties, including the symmetric, reversible, ZCn, zip, and 2-primal property, transfer between R and the skew polynomial ring Rx; α, δ], in case R is (α, δ)-compatible skew-Armendariz. As a consequence we extend and unify several known results. |
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Keywords: | Armendariz ring Ore extension Prime radical |
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