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Topic: unique prime factorization
Replies: 8   Last Post: Dec 5, 2010 12:44 PM

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davide

Posts: 6
From: paris
Registered: 11/26/05
unique prime factorization
Posted: Sep 4, 2009 7:28 AM
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Dear all,

I would like to ask the following question. Please, correct me if you find errors in formulation, or if it is unclear:

Consider the ring arising from the ring of integers in Q(a, b, c...) by adjunction of square roots. Q(a, b, c....) being the field of the rational functions of the indeterminates a, b, c ...

Does this ring lack unique prime factorization? and why?


Despite of its purely mathematical character, this problem has an historical interest, since it allows to clarify descartes' theory of equations, and in particular, his technique of reducibility.


Thank you everyone,

Bests
Davide



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