On Annihilator Multiplication Modules

An A-module E is an annihilator multiplication module if, for each e∈ E, there is a finitely generated ideal I of A such that $ann(e)=ann(IE)$. In this paper, we investigate fundamental properties of annihilator multiplication modules and employ them as a framework for characterizing significant classes of rings and modules, including torsion-free modules, multiplication modules, injective modules, and principal ideal von Neumann regular rings. In addition, we establish that, for such modules, the equality AssA(E)=Ass(A) holds, thereby providing a precise connection between module-theoretic and ring-theoretic prime structures.