On annihilators in skew extensions of rings

According to Jacobson, a right ideal is bounded if it contains a non-zero ideal, and called a ring is called strongly right bounded if every non-zero right ideal is bounded. A ring is strongly right AB if every non-zero right annihilator is bounded. In this paper, we introduce and investigate a particular class of McCoy rings which satisfy the conditions asked by Nielsen. We assume that R is an (α,δ)-compatible ring, and prove that, if R is reversible then the Ore extension R[x; α; δ] is strongly right AB. It is also shown that, every right duo ring with an automorphism α is skew McCoy