20121231, 06:22  #1 
Dec 2003
Hopefully Near M48
3336_{8} Posts 
Factorization of Ideals in Number Field, Looking for Reference
Let K be the number field . Find the factorizations of (7), (29) and (31) in .
I know there's a theorem by Kronecker that says (7) is reducible iff , 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 
20121231, 19:49  #2 
Dec 2012
The Netherlands
2^{7}×13 Posts 

20130102, 06:17  #3 
Dec 2003
Hopefully Near M48
2·3·293 Posts 
Thanks. I presume 'rational integer' and 'rational prime' mean 'element of ' and 'prime in ' respectively? As opposed to 'element of ' and 'prime in '?
Last fiddled with by jinydu on 20130102 at 06:19 
20130102, 09:44  #4  
Dec 2012
The Netherlands
2^{7}·13 Posts 
Quote:
in algebraic number theory, the elements of are called rational integers to distinguish them from algebraic integers, and similarly with primes. 

20130102, 18:09  #5 
Dec 2003
Hopefully Near M48
1758_{10} Posts 

20140730, 11:24  #6  
Nov 2003
2^{2}×5×373 Posts 
Quote:


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