Invariant factor
The invariant factors of a module over a principal ideal domain occur in one form of the structure theorem for finitely generated modules over a principal ideal domain.
If is a PID and a finitely generated -module, then
for some integer and a list of nonzero elements for which. The nonnegative integer is called the free rank or Betti number of the module, while are the invariant factors of 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.
