ON SKEW ARMENDARIZ AND SKEW QUASI-ARMENDARIZ MODULES

Let α be an endomorphism and α an α-derivation of a ring R. In this paper we study the relationship between an R-module MR and the general polynomial module M[x] over the skew polynomial ring R[x; α, δ]. We introduce the notions of skew-Armendariz modules and skew quasi-Armendariz modules which are generalizations of α-Armendariz modules and extend the classes of non-reduced skew-Armendariz modules. An equivalent characterization of an α-skew Armendariz module is given. Some properties of this generalization are established, and connections of properties of a skew-Armendariz module MR with those of M[x] R[x; α, δ] are investigated. As a consequence we extend and unify several known results related to Armendariz modules.