Answer to Question #147955 in Abstract Algebra for Sourav Mondal

Question #147955
Prove that Z[√-3 ] is not a U.F.D
1
Expert's answer
2020-12-01T15:04:48-0500

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


4=22=(1+3)(13)4 = 2*2 = (1+\sqrt{-3}) *(1 - \sqrt{-3})


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


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


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