Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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.

share|improve this question
    
There was an MO question about this, but I can't find it. –  Qiaochu Yuan Sep 24 '10 at 0:39
2  
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 at 14:35
    
@Weaam I wonder if the proof Milne refers to directly generalizes :) –  rschwieb Aug 1 at 14:39

1 Answer 1

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.)

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.