In this paper, we introduce the notion of weak Armendariz module as a generalization of the notion of an Armendariz module and investigate properties of such modules. We prove that if M is a torsion-free module over a domain R, then for any n, is a weak Armendariz module over We also show that finite direct products of weak Armendariz modules are weak Armendariz. Examples of weak Armendariz modules which are not Armendariz are given.

Armendariz rings, weak Armendariz ring, Armendariz module, weak Armendariz module.