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.
Yiqiang ZHOU. Michał ZIEMBOWSKI. "Distributive modules and Armendariz modules." J. Math. Soc. Japan 67 (2) 789 - 796, April, 2015. https://doi.org/10.2969/jmsj/06720789