20121231, 06:22  #1 
Dec 2003
Hopefully Near M48
1758_{10} 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
2×7×113 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
11000101110_{2} 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
2·3·293 Posts 

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


Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Basic Number Theory 21: ideals and homomorphisms  Nick  Number Theory Discussion Group  5  20170604 12:36 
Theorems about ideals  fivemack  Abstract Algebra & Algebraic Number Theory  10  20120122 11:01 
NFS reference  Jushi  Math  2  20060828 12:07 
Factorization attempt to a c163  a new Odd Perfect Number roadblock  jchein1  Factoring  30  20050530 14:43 
Number with small factor: Further factorization?  Mystwalker  GMPECM  3  20050502 08:31 