Ore extensions of skew $pi$-Armendariz rings

Lunqun, O.; Jingwang, L.; Yueming, X.

Ore extensions of skew $pi$-Armendariz rings

Document Type : Research Paper

Authors

O. Lunqun ¹

L. Jingwang ²

X. Yueming ³

¹ Department of Mathematics, Hunan University of Science and Technology, Xiangtan, Hunan 411201, P.R. China

² Department of Mathematics, Hunan University of Science and Technology Xiangtan, Hunan 411201, P. R. China

³ Department of Mathematics and Applied Mathematics, Huaihua University, Huaihua, 418000, P. R. China

Abstract

For a ring endomorphism
$alpha$ and an $alpha$-derivation $delta$, we introduce a
concept, so called skew $pi$-Armendariz ring, that is a
generalization of both $pi$-Armendariz rings,
and $(alpha,delta)$-compatible skew Armendariz rings. We first
observe the basic properties of skew $pi$-Armendariz rings, and
extend the class of skew $pi$-Armendariz rings through various ring
extensions. We next show that all $(alpha,delta)$-compatible
$NI$ rings are skew $pi$-Armendariz, and if a ring $R$ is an
$(alpha,delta)$-compatible $2$-$primal$ ring, then the polynomial
ring $R[x]$ is skew $pi$-Armendariz.

Keywords

skew Armendariz ring

skew $pi$-Armendariz ring

$pi$-Armendariz ring

Subjects