Distributive modules and Armendariz modules

抄録

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.