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Old 2012-12-31, 06:22   #1
jinydu
 
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Dec 2003
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Default Factorization of Ideals in Number Field, Looking for Reference

Let K be the number field \mathbb{Q}(2^{1/3}). Find the factorizations of (7), (29) and (31) in O_K.

I know there's a theorem by Kronecker that says (7) is reducible iff x^3\equiv 2 \text{mod }7, has a solution (or something like that) and how to find the factorization in the case it does have a solution. But I can't seem to find a reference for this.

Can anyone suggest a reference? No spoilers to this problem please, just a reference.

Thanks
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