- #1

Math Amateur

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Can someone demonstrate a proof of this proposition ... or point me to a text or online notes that contain a proof ...

Help will be appreciated ... ...

Peter

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- #1

Math Amateur

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Can someone demonstrate a proof of this proposition ... or point me to a text or online notes that contain a proof ...

Help will be appreciated ... ...

Peter

- #2

fresh_42

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For ##K[X]## you know that you can apply the Euclidean algorithm (division) to find all irreducible factors of a polynomial.

- #3

Math Amateur

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For ##K[X]## you know that you can apply the Euclidean algorithm (division) to find all irreducible factors of a polynomial.

Hmm ... yes, get the general idea ... but not quite sure how the induction is set up and how exactly it proceeds ... Thinking ...

Thanks for the help ...

Peter

- #4

fresh_42

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The induction step is: If a ring ##R## is UFD, so is ##R[X]##.Hmm ... yes, get the general idea ... but not quite sure how the induction is set up and how exactly it proceeds ... Thinking ...

Thanks for the help ...

Peter

(See http://math.harvard.edu/~waffle/ufds2.pdf [Broken]) This brief article also contains a pretty good overview on some frequent classes of rings. I think you should read it to gain a feeling for the concepts and a pool of examples (14 pages).

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- #5

Math Amateur

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The induction step is: If a ring ##R## is UFD, so is ##R[X]##.

(See http://math.harvard.edu/~waffle/ufds2.pdf [Broken]) This brief article also contains a pretty good overview on some frequent classes of rings. I think you should read it to gain a feeling for the concepts and a pool of examples (14 pages).

Thanks fresh_42 ... ... most helpful ... appreciate the help ...

Peter

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- #6

mathwonk

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auslander and buchsbaum were among the foremost experts of unique factorization domains. their graduate algebra book, is available free here ( see e.g. chapter 5):

https://babel.hathitrust.org/cgi/pt?id=mdp.39015015615886;view=1up;seq=10

my own discussion is in sections 4,5 of these free class notes.

http://alpha.math.uga.edu/~roy/844-1.pdf

and by the way Buchsbaum is apparently still active:

http://people.brandeis.edu/~buchsbau/

https://babel.hathitrust.org/cgi/pt?id=mdp.39015015615886;view=1up;seq=10

my own discussion is in sections 4,5 of these free class notes.

http://alpha.math.uga.edu/~roy/844-1.pdf

and by the way Buchsbaum is apparently still active:

http://people.brandeis.edu/~buchsbau/

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