Abstract

Let M be a finitely-generated module over a Noetherian ring R. Suppose 𝔞 is an ideal of R and let N=𝔞M and 𝔟=Ann(M/N). If 𝔟J(R), M is complete with respect to the 𝔟-adic topology, {Pi}i1 is a countable family of prime submodules of M, and xM, then x+Ni1Pi implies that x+NPj for some i1. This extends a theorem of Sharp and Vámos concerning prime ideals to prime submodules.