ORE EXTENSIONS OF 2-PRIMAL RINGS

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 Ni`(R) = Ni`∗(R;α, δ) if and only if Ni`(R)[x;α, δ] = Ni`∗(R[x;α, δ]) if and only if every minimal (α, δ)-prime ideal of R is completely prime.