Finitely Content Modules

Let R be a commutative ring with identity and M be a unitary R-module. We define M to be a n finitely content module if for each finite set {I1, · · · , In} of ideals of R, ( ∩ Iλ)M = n (IλM ). The class of λ=1 content modules contains the class of finitely content modules properly. It is shown that that every module over a Pru¨fer domain or a valuation ring is finitely content.