 By changing the choice of generating set, one can in fact describe the module as the quotient of some "Rn" by a particularly simple submodule, and this is the structure theorem.The structure theorem for finitely generated modules over a principal ideal domain usually appears in the following two forms.For every finitely generated module over a principal ideal domain , there is a unique decreasing sequence of proper ideals formula_1 such that is isomorphic to the sum of cyclic modules