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

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 a ∈ P (R) for a ∈ R, 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 a ∈ R. 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). Mathematics subject classification: 16S36, 16N40, 16P40, 16S32, 16W20, 16W25.