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Which of the following integral domains are Euclidean domains?

  1. $\mathbb{Z}[\sqrt{-3}]$
  2. $\mathbb{Z}[x]$
  3. $\mathbb{R}[x^2,x^3]=\{f=\sum_{i=0}^n a_ix^i\in\mathbb{R}[x]:a_1=0\}$
  4. $(\mathbb{Z}[x]/(2,x))[y]$

How can we solve this problem. Can anyone suggest me something. Thanks

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    To show that something is a ED, find a Euclidean function. To show thta something isn't, e.g show that it's not a PID.2012-12-17
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    @priti: Something is very strange in you definition of (3)2012-12-17
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    @AlexB., ok if it works, but there are PIDs that are not Euclidean: http://en.wikipedia.org/wiki/Principal_ideal_domain#Properties2012-12-17

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