Annihilator conditions on polynomials over modules. (Q545473)

Let \(R\) be a ring with unity and \(M\) a right \(R\)-module. In this paper the author defines an action of the nearring \((R[x],+,\circ)\) on the additive group \(M[x]\) of polynomials over \(M\), and tries to study the Baer type annihilator conditions on \(M[x]\). However, the action does not make \(M[x]\) an \(R[x]\)-module since \(R[x]\) is not commutative under the composition operation (even when \(R\) is commutative).