Let $alpha$ be an endomorphism and $delta$ an $alpha$-derivation of a ring $R$. In this paper we study the relationship between an $R$-module $M_R$ and the general polynomial module $M[x]$ over the skew polynomial ring $R[x;alpha,delta]$. We introduce the notions of skew-Armendariz modules and skew quasi-Armendariz modules which are generalizations of $alpha$-Armendariz modules and extend the classes of non-reduced skew-Armendariz modules. An equivalent characterization of an $alpha$-skew Armendariz module is given. Some properties of this generalization are established, and connections of properties of a skew-Armendariz module $M_R$ with those of $M[x]_{R[x;alpha,delta]}$ are investigated. As a consequence we extend and unify several known results related to Armendariz modules.
Alhevaz, A., & Moussavi, A. (2012). On skew Armendariz and skew quasi-Armendariz
modules. Bulletin of the Iranian Mathematical Society, 38(1), 55-84.
MLA
A. Alhevaz; A. Moussavi. "On skew Armendariz and skew quasi-Armendariz
modules". Bulletin of the Iranian Mathematical Society, 38, 1, 2012, 55-84.
HARVARD
Alhevaz, A., Moussavi, A. (2012). 'On skew Armendariz and skew quasi-Armendariz
modules', Bulletin of the Iranian Mathematical Society, 38(1), pp. 55-84.
VANCOUVER
Alhevaz, A., Moussavi, A. On skew Armendariz and skew quasi-Armendariz
modules. Bulletin of the Iranian Mathematical Society, 2012; 38(1): 55-84.