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!