SI-rings and their extensions as 2-primal rings

Abstract

Let R be a ring, σ an automorphism of R such that aσ(a) ∈ N(R) if and only if a ∈ N(R), where N(R) is the set of nilpotent elements of R and δ a σ-derivation of R such that δ(P) ⊆ P, for all minimal prime ideal P of R. We recall that a ring R is called an SI-ring if for a, b ∈ R, ab = 0 implies aRb = 0. In this paper we show that if R is a commutative Noetherian SI-ring, which is also an algebra over Q and σ and δ be as above, then R[x;σ,δ] is 2-primal.