Completely generalized right primary rings and their extensions

Abstract

A ring $R$ is said to be a completely generalized right primary ring ($c.g.r.p$ ring) if $a, b \in R$ with $ab = 0$ implies that $a = 0$ or $b$ is nilpotent. Let now $R$ be a ring and $\sigma$ an automorphism of $R$. In this paper we extend the property of a completely generalized right primary ring ($c.g.r.p$ ring) to the skew polynomial ring $R[x;\sigma]$.