Let us consider the rational number field $ \mathbb{Q}$ and its finite extension $ K$.
I can't understand the concept of large ramification index or enough Ramification or sufficient Ramification.
Let $A$ be Dedekind domain, $K$ be its fraction field and let $L$ be finite extension of $K$ of degree $n$. Let $B$ be the integral closure of $A$.
Let $P$ be a nonzero prime ideal of $A$. The lofting (also called extension) of $P$ to $B$ is the ideal $PB$. Now the ideal $PB$ may not be prime ideal of $B$ but since it is a Dedekind domain , we can express it as a product of prime ideals in $B$ i.e., $$ PB=\prod_{i=1}^{g} P_i^{e_i} $$ where $P_i$ are distinct prime ideals of $B$ and $e_i$ are positive integers.
This Phenomenon is called Ramification.
But my question is what is Enough Ramification or large ramification (index)?
Please explain this fact with one example.
Thanks