On 2-primal Ore extensions

Abstract

Let R be a ring, be an automorphism of R and δ be a σ-derivation of R. We define a δ property on R. We say that R is a δ-ring if aδ(a) ∊ P(R) implies a ∊ P(R), where P(R) denotes the prime radical of R. We ultimately show the following. Let R be a Noetherian δ-ring, which is also an algebra over Q, σ and δ be as usual such that σ(δ(a)) = δ(σ(a)), for all a ∊ R and σ(P) = P, P any minimal prime ideal of R. Then R[x, σ(, δ] is a 2-primal Noetherian ring.