ANNIHILATOR CONDITIONS ON NEARRING OF SKEW POLYNOMIALS OVER A RING

Abstract

Let $R$ be a ring with unity. For a ring endomorphism $\alpha$ and an $\alpha$-derivation $\delta$, the system $R[x;\alpha,\delta]$ forms an abelian nearring under addition and substitution operations. In this paper we extend the study of annihilator conditions on nearring of polynomials to skew nearring ($R[x;\alpha,\delta]$, $+$, $\circ$), when $R$ is an $\alpha$-rigid ring. Also, we give a characterization of $\alpha$-rigid rings. An example to show that ``$\alpha$-rigid condition on $R$" is not superfluous is given.