The module is determined up to isomorphism by specifying its free rank , and for class of associated irreducible elements  and each positive integer  the number of times that  occurs among the elementary divisors. The elementary divisors can be obtained from the list of invariant factors of the module by decomposing each of them as far as possible into pairwise relatively prime (non-unit) factors, which will be powers of irreducible elements.
The module is determined up to isomorphism by specifying its free rank, and for each class of associated irreducible elements and each positive integer, the number of times it occurs among the elementary divisors. The elementary divisors can be obtained from the list of invariant factors of the module by decomposing each of them as far as possible into pairwise relatively prime (non-unit) factors, which will be powers of irreducible elements.