Smith Normal Form for PIDs

Question

Could someone provide a good reference to look up the existence and uniqueness of Smith Normal Form (SNF) for a PID?

I have seen it done for Euclidean domains but not for a PIDs. I know the difference is not much, but I would like a good reference. Thanks.

Answer 1

See Hungerford, Algebra, 1974, Proposition 2.11, page 339.

Answer 2

See Jacobson's Basic Algebra I, chapter 3.

See also the book Finitely Generated Abelian Groups and Similarity of Matrices over a Field by Christopher Norman.