# Ore extensions of skew $pi$-Armendariz rings

Document Type : Research Paper

Authors

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.

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Main Subjects

### History

• Receive Date: 14 May 2011
• Revise Date: 29 June 2011
• Accept Date: 29 June 2011