# On annihilator ideals in skew polynomial rings

Document Type : Research Paper

Authors

Department of Pure Mathematics‎, ‎Faculty of Mathematical Sciences‎, ‎Tarbiat Modares University‎, ‎P.O‎. ‎Box 14115-134‎, ‎Tehran‎, ‎Iran.

Abstract

This article examines annihilators in the skew polynomial ring $R[x;alpha,delta]$. 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 Property ($A$) and the conditions asked by P.P. Nielsen. We assume that $R$ is an ($alpha$,$delta$)-compatible ring, and prove that, if $R$ is nil-reversible then the skew polynomial ring $R[x;alpha,delta]$
is strongly right $AB$. It is also shown that, every right duo ring with an automorphism $alpha$ is skew McCoy. Moreover, if $R$ is strongly right $AB$ and skew McCoy, then $R[x;alpha]$ and $R[x;delta]$ have right Property ($A$).

Keywords

Main Subjects

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### History

• Receive Date: 30 September 2014
• Revise Date: 17 October 2015
• Accept Date: 31 March 2016