# Proofs of the structure theorem for finitely generated modules over a PID

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.

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There was an MO question about this, but I can't find it. –  Qiaochu Yuan Sep 24 '10 at 0:39
Perhaps you meant this question about finitely generated abelian groups. mathoverflow.net/questions/12009/… –  Weaam Sep 24 '10 at 0:44
I think Jacobson's proofs in Basic Algebra I are a good baseline. I don't know that anything written there is particularly elegant, but I think it's relatively elementary. –  rschwieb Aug 1 '14 at 14:35
@Weaam I wonder if the proof Milne refers to directly generalizes :) –  rschwieb Aug 1 '14 at 14:39