Talk:Unique factorization

Article Checklist for "Unique factorization"

Workgroup category or categories	Mathematics Workgroup [Categories OK]
Article status	Developing article: beyond a stub, but incomplete
Underlinked article?	No
Basic cleanup done?	Yes
Checklist last edited by	Greg Martin 22:17, 29 April 2007 (CDT)

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could be a good article

Right now this article only discusses unique factorization of integers - and that's definitely the most important sense of the words "unique factorization". However, there are other mathematical objects for which unique factorization is an important concept: polynomial rings and rings of integers in number fields (such as $\mathbb {Z} [i]$) come immediately to mind. The latter concept, which began to be investigated in relation to early attempts to prove Fermat's Last Theorem, eventually led to the definition of ideals in rings. Anyway, consider this an invitation to be bold and expand the current article. - Greg Martin 22:19, 29 April 2007 (CDT)

If I remember right, if you extend the integers by including ${\sqrt {-3}}$ you get a ring which does not have unique prime factorization. --Catherine Woodgold 20:42, 30 April 2007 (CDT)

induction?

Note that the proof currently given is not formally a proof by induction: instead it uses the phrase "Continuing in this way". We should choose one or the other. - Greg Martin 22:21, 29 April 2007 (CDT)