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#### bw0young0math

##### New member

- Jun 14, 2013

- 27

I learned Z[root(-3)] is not UFD.

Then Z[root(-3)] is a example about gcd-domain( there exist some elts a,b in domain D such that it does not exist gcd(a,b).)

Let a=2, b-1+root(-3) .

a and b are not associates and they just have common divisor 1 and -1.

So gcd(a,b) does not exist.

Hum..... I don't know why associate, 1/-1 have some relations with not existing gcd. Please...............................