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.
