Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Suppose we have a Dedekind domain $R$ which for the moment we can take to be $\mathcal{O}_K$ for some algebraic number field $K$. Now suppose that $Q_1,Q_2$ are prime ideals that lie over a prime ideal $p$ of $\Bbb{Z}$. This means that $Q_1\cap \Bbb{Z} = p$, $Q_2\cap \Bbb{Z} = p$. Is it true that

$$Q_1Q_2 \cap \Bbb{Z} = p^2?$$

I can see that one containment is true, namely that $p^2 \subseteq Q_1Q_2 \cap \Bbb{Z}$.

share|improve this question
add comment

1 Answer

up vote 1 down vote accepted

Try $Q_1=(3,1+\sqrt{-5})$, $Q_2=(3,1-\sqrt{-5})$.

share|improve this answer
    
Yes I see that $Q_1Q_2 \cap \Bbb{Z} = 3$. Thanks for your answer. The reason why I asked this because I thought it could be used to prove my problem here. –  fpqc Jan 6 '13 at 4:27
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.