Lunqun, O., Jingwang, L., Yueming, X. (2013). Ore extensions of skew $pi$-Armendariz rings. Bulletin of the Iranian Mathematical Society, 39(2), 355-368.

O. Lunqun; L. Jingwang; X. Yueming. "Ore extensions of skew $pi$-Armendariz rings". Bulletin of the Iranian Mathematical Society, 39, 2, 2013, 355-368.

Lunqun, O., Jingwang, L., Yueming, X. (2013). 'Ore extensions of skew $pi$-Armendariz rings', Bulletin of the Iranian Mathematical Society, 39(2), pp. 355-368.

Lunqun, O., Jingwang, L., Yueming, X. Ore extensions of skew $pi$-Armendariz rings. Bulletin of the Iranian Mathematical Society, 2013; 39(2): 355-368.

^{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

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

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.