Distributive modules and Armendariz modules

Abstract

Motivated by a recent result of Mazurek and Ziembowski in [ 21] that every left distributive ring is Armendariz, in this paper we present methods of constructing Armendariz modules using a distributive module. We prove that, for a bimodule $_RV_A$, $_RV$ being distributive implies that $V_A$ is Armendariz, and that every right module over a right distributive ring is Armendariz. These results can be used to construct new Armendariz rings. Examples are provided to illustrate and delimit the results obtained.