Department of Mathematics, Hunan University of Science and
Technology,
Xiangtan, Hunan 411201, 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.
Top