Can someone check this for me?

Thread starter omega16
Start date Oct 25, 2006

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The prime factorization of 6 in the field Q[sqrt(-1)] is expressed as 6 = (1+sqrt(-1))(1-sqrt(-1)) * 3. The discussion confirms that 2 and 3 are prime numbers, while questioning the primality of 1+sqrt(-1) and 1-sqrt(-1) in this context. Participants seek clarification on whether additional information is needed to complete the problem. The conversation emphasizes understanding the nature of prime elements in the given field. Overall, the factorization appears to be correct, and the inquiry about completeness suggests a desire for validation.

Oct 25, 2006

omega16

Find the prime factorization of 6 in Q[sqrt(-1)].

Ans : Since 6 = 2*3
so 6 = (1+sqrt(-1)) (1-sqrt(-1)) *3 Q.E.D.

Do I need to add anything to it? Am I done with this question? Please kindly advise me. Thank you very much.

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Oct 25, 2006

StatusX

Homework Helper

How do you know those are prime?

Oct 25, 2006

omega16

because 2 and 3 are prime.

Oct 25, 2006

StatusX

Homework Helper

I mean 1+sqrt(-1), 1-sqrt(-1), and 3 in the field Q(sqrt(-1)).

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