The invariant factors of a module over a principal ideal domain (PID) occur in one form of the structure theorem for finitely generated modules over a principal ideal domain.

is a PID a finitely generated-module, then

is called the free rank or Betti number are the invariant factors and are unique up to associatedness.

The invariant factors of a matrix over a PID occur in the Smith normal form and provide a means of computing the structure of a module from a set of generators and relations.

See also

• Elementary divisors

References

• Chap.8, p.128.

• Chapter III.7, p.153 of