Abstract. We examine the properties of certain mappings between the lattice of ideals of a commutative ring R and the lattice of submodules of an R-module M , in particular considering when these mappings are lattice homomorphisms. We prove that the mapping λ from the lattice of ideals of R to the lattice of submodules of M defined by λ(B) = BM for every ideal B of R is a (lattice) isomorphism if and only if M is a finitely generated faithful multiplication module. Moreover, for certain but not all rings R, there is an isomorphism from the lattice of ideals of R to the lattice of submodules of an R-module M if and only if the mapping λ is an isomorphism.Mathematics Subject Classification (2010): 06B99, 13F05, 13E05, 13C99