(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let K be a number field. Let a be an irreducible element of K. Prove that if <a>(the ideal generated by a) is not a prime ideal, then it is a product of two prime ideals.

2. Relevant equations

3. The attempt at a solution

I'm actually quite clueless... I have been thinking maybe it is possible for me to obtain some information about the extension K:Q from the condition that the class number is 2, like the degree of the extension, etc..?

Any help is appreciated!

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# Homework Help: Factor principal ideals in a field with class number 2

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