Journal of the
Korean Mathematical Society JKMS

For a ring endomorphism $\alpha$ and an $\alpha$-derivation $\delta$, we introduce $(\alpha,\delta)$-skew Armendariz rings which are a generalization of $\alpha$-rigid rings and Armendariz rings, and investigate their properties. A semiprime left Goldie ring is $\alpha$-weak Armendariz if and only if it is $\alpha$-rigid. Moreover, we study on the relationship between the Baerness and p.p. property of a ring $R$ and these of the skew polynomial ring $R[x;\alpha,\delta]$ in case $R$ is $(\alpha,\delta)$-skew Armendariz. As a consequence we obtain a generalization of [11], [14] and [16].

Keywords: Baer rings, right p.p.-rings, $\alpha$-rigid rings, $(\alpha,\delta)$-Armendariz rings

MSC numbers: 16D15, 16D40, 16D70