Answer to Question #147955 in Abstract Algebra for Sourav Mondal

Abstract Algebra

Question #147955

Prove that Z[√-3 ] is not a U.F.D

Expert's answer

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)

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