ON SKEW ARMENDARIZ AND SKEW QUASI-ARMENDARIZ MODULES

Let be an endomorphism and an -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;, ). We introduce the notions of skew- Armendariz modules and skew quasi-Armendariz modules which are generalizations of -Armendariz modules and extend the classes of non-reduced skew-Armendariz modules. An equivalent charac- terization of an -skew Armendariz module is given. Some proper- ties of this generalization are established, and connections of prop- erties of a skew-Armendariz module MR with those of M(x)R(x;, ) are investigated. As a consequence we extend and unify several known results related to Armendariz modules.

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