Answer to Question #147955 in Abstract Algebra for Sourav Mondal

Question

Prove that Z[√-3 ] is not a U.F.D

Answer 1

Let consider the number 4 from $Z[\sqrt{-3} ]$

$4 = 2*2 = (1+\sqrt{-3}) *(1 - \sqrt{-3})$

So 4 is not uniquely factorized in $Z[\sqrt{-3} ]$ .

Hence $Z[\sqrt{-3} ]$ is not a U.F.D (Unique Factorization Domain)