From: David Bernier <bernier@my-deja.com>
Subject: Re: My FLT proof: Keeping things simple
Date: Tue, 03 Oct 2000 07:35:52 GMT
Newsgroups: sci.math
Summary: [missing]

In article <8r6ue3$ah3$1@freenet9.carleton.ca>,
  ah170@FreeNet.Carleton.CA (David Libert) wrote:
[...]
>   Anyway, I will present another failure of UFD among linear
> polynomials, over coefficients in a quadratic extension of Z:
>
> (X+3)(X+1)  =   X^2 + 4X + 3  =   (X + 2+i) (X + 2-i)    where i^2 = -1.
>
> Ie, this is in polynomials over Z[i],  and the  2+i  and 2-i  are
> respective constant coefficients.
[...]

I get  (X + 2+i) (X + 2-i) = X^2 + 4X + 5
There is an interesting page about quadratic fields and their
rings of integers at:
http://www.ams.org/new-in-math/cover/factorization.html

If D= {a+bi, a, b in Z}  (the Gaussian integers), then D is
a UFD with units +/-1 , +/-i.  I think it follows that D[x],
the ring of polynomials with coefficients in D, is also a UFD.

David



Sent via Deja.com http://www.deja.com/
Before you buy.