As dual to the notion of “finitely injective modules” introduced and studied by Ramamurth and Rangaswamy (1973), we define a right R-module M to be finitely projective if it is projective. with respect to short exact sequences of right R-modules of the form 0 → A → B → C → 0 with C finitely generated. We have completely characterized finitely projective modules over a Dedekind domain. If R is a Dedekind domain, then an R-module M is finitely projective if and only if its reduced part is torsionless and coseparable.

For a Dedekind domain R, finite projectivity, unlike projectivity is not hereditary. But it is proved to be pure hereditary, that is, every pure submodule of a finitely projective R-module is finitely projective.