 Therefore, if "M" is in addition a locally free "O""X"-module, giving "M" a "D"-module structure is nothing else than equipping the vector bundle associated to "M" with a flat (or integrable) connection.As the ring "D""X" is noncommutative, left and right "D"-modules have to be distinguished.However, the two notions can be exchanged, since there is an equivalence of categories between both types of modules, given by mapping a left module "M" to the tensor product "M" ⊗ Ω"X", where Ω"X" is the line bundle given by the highest exterior power of differential 1-forms on "X".