mersenneforum.org - View Single Post - Factorization of Ideals in Number Field, Looking for Reference

jinydu · 2012-12-31, 06:22

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

2012-12-31, 06:22	#1
jinydu Dec 2003 Hopefully Near M48 2×3×293 Posts	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