I'm looking for different proofs (references or sketch of main ideas) of the structure theorem for finitely generated modules over a PID.
If possible, a comparison in terms of clarity, elegance or usefulness would be appreciated.
Fred Goodman has a freely downloadable algebra text that contains this result in section 8.5. Unfortunately, I am not knowledgeable enough to offer a useful comparison to other references. But hey, it's free!
(I studied draft versions of this material as it was being written. I was taking a class from the author, and I found it useful. It became "Edition 2.5" with substantial additions because the 2nd Edition didn't have enough to cover the full first-year graduate level algebra sequence at Iowa.)