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IMCS/Publications/BASM/Issues/BASM n.1 (65), 2011/

On 2-primal Ore extensions over Noetherian σ(*)-rings

Authors: Vijay Kumar Bhat

Abstract

In this article, we discuss the prime radical of skew polynomial rings over Noetherian rings. We recall σ(*) property on a ring R (i.e. aσ(a)∈P(R) implies aP(R) for aR, where P(R) is the prime radical of R, and σ an automorphism of R). Let now δ be a σ-derivation of R such that δ(σ(a)) = σ(δ(a)) for all aR. Then we show that for a Noetherian σ(*)-ring, which is also an algebra over {Q}, the Ore extension R[x; σ, δ] is 2-primal Noetherian (i.e. the nil radical and the prime radical of R[x; σ, δ] coincide).

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