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Let $L=\mathbb{Q}(\sqrt{-5}, i)$ and $K=\mathbb{Q}(\sqrt{-5})$. Let $O_K$ and $O_L$ be the rings of algebraic integers of $K$ and $L$. I want to find out the prime factorization of the ideal generated by $2$ and $5$ in $O_K$ and $O_L$ ?

How to do this ?

Let $L=\mathbb{Q}(\sqrt{-5}, i)$ and $K=\mathbb{Q}(\sqrt{-5})$. Let $O_K$ and $O_L$ be the rings of algebraic integers of $K$ and $L$. It can be checked that

$$2O_K=\langle 2, \sqrt{-5}+1\rangle^2$$

I want to find out the prime factorization of the ideal generated by $2$ and $5$ $\langle 2, \sqrt{-5}+1\rangle O_L$ in $O_K$ and $O_L$ ?

How The problem I am having is this. I don't know the syntax for the ideal generated by $\langle 2, \sqrt{-5}+1\rangle O_L$.

What to do this ?