Multiplication modules which are distributive (Q1111618)

An R-module M over a commutative ring R with identity is said to be multiplicative, if every submodule of M is of the form IM, for some ideal I of R. An R-module N is said to be distributive, if every submodule of N is distributive. The author proves several results which relate the notion of distributive and multiplicative modules, e.g. a finitely generated faithful module M over a ring R is distributive if and only if M is a multiplicative module and R considered as a module over itself is distributive.