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- Path: sparky!uunet!dziuxsolim.rutgers.edu!spade.rutgers.edu!cadet
- From: cadet@spade.rutgers.edu (Uniquely TiJean)
- Newsgroups: sci.math
- Subject: factorization in commutative rings
- Message-ID: <Jan.3.02.05.44.1993.24643@spade.rutgers.edu>
- Date: 3 Jan 93 07:05:44 GMT
- Distribution: sci.math
- Organization: Rutgers Univ., New Brunswick, N.J.
- Lines: 26
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- Well, Given D an integral domain
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- Then D = euclidean domain ==> D = principal ideal domain ==> D = factorial
- domain.
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- I am looking for counterexamples
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- A) D= factorial domain doesn't imply D= princ. idl. domain
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- Standard example Z[x] or F[x,y] where F=field
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- B) D= princ. idl. domain doesn't imply D= euclidean domain.
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- Well, I found in Hungerford ( Algebra )
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- the following Z( (1+sqrt(-19)) / 2 )
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- Question: How come? I have no cue as to why the above domain isn't euclidean.
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- Any suggestion is appreciated.
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- Happy New Year!
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- JC
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- PS. I am preparing for my quals so that's why I asked.
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