Ore extensions of 2-primal rings

Abstract

Let R be a ring with an endomorphism α and an α-derivation δ. In this note we show that if R is (α, δ)-compatible then R is 2-primal if and only if the Ore extension R[x; α, δ] is 2-primal if and only if Niℓ(R) = Niℓ*(R; α, δ) if and only if Niℓ(R)[x; α, δ] = Niℓ*(R[x; α, δ]) if and only if every minimal (α, δ)-prime ideal of R is completely prime. © World Scientific Publishing Company.