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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.2010-09-24
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    Perhaps you meant this question about finitely generated abelian groups. http://mathoverflow.net/questions/12009/is-there-a-slick-proof-of-the-classification-of-finitely-generated-abelian-groups2010-09-24
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    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.2014-08-01
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    @Weaam I wonder if the [proof Milne refers to](http://mathoverflow.net/a/12135/19965) directly generalizes :)2014-08-01

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