Ramification in algebraic number theory means prime numbers factoring into some repeated prime ideal factors.
Ramification in algebraic number theory means prime numbers factoring into some repeated prime ideal factors. For instance, if $p$ is a rational prime and $K / \Bbb Q$ a number field, then $p$ ramifies in $K$ if $p \mathcal{O}_K$ decomposes as a product of prime ideals $\prod\limits_{i=1}^m P_i^{e_i}$ so that there is some index $i$ such that $e_i \geq 2$.
