On annihilator ideals in skew polynomial rings

This article examines annihilators in the skew polynomial ring R[x; α, δ]. A ring is strongly right AB if every non-zero right annihilator is bounded. In this paper, we introduce and investigate a class of McCoy rings which satisfies Property (A) and the proposed conditions by P.P. Nielsen [J. Algebra 298 (2006) 134-141]. We assume that R is an (α,δ)-compatible ring, and prove that, if R is nil-reversible then the skew polynomial ring R[x; α, δ] is strongly right AB. It is also shown that, every right duo ring with an automorphism α is skew McCoy. Moreover, if R is strongly right AB and skew McCoy, then R[x; α] and R[x; δ] have right Property (A).