Let $K$ be an algebraic extension of the rational numbers and $L$ an algebraic extension of $K$. Let $\mathfrak{a}_K = (a, \alpha )$ be an ideal of the ring of integers $\mathcal{O}_K$ of $K$, with $a \in \mathbb{Z}$ and $\alpha \in \mathcal{O}_K$. Let $\mathfrak{a}_L = (a, \alpha )$ be an ideal of the ring of integers $\mathcal{O}_L$ of $L$. By $\mathfrak{a}_L$, I mean simply $\mathfrak{a}_K$ taken as an ideal of $\mathcal{O}_L$.
What is the relationship between the norms $[\mathcal{O}_L : \mathfrak{a}_L]$ and $[\mathcal{O}_K : \mathfrak{a}_K]$ and what is a reference for this result?