I'm reading this pdf which is showing that a rational prime $p$ ramifies if and only if it divides the discriminant of its number field $K$. I've come across the following line:
Let $p \in \mathbb Z$ be a prime and let $a_1, \dots, a_n$ be a $\mathbb Z$ basis for $A$. Then of course $\overline{a_1}, \dots, \overline{a_n}$ is a $k(\mathfrak p)$ basis for $A/pA$.
Here $A$ is the ring of integers of $K$. My question: what does $k(\mathfrak p)$ mean, and why is this statement true?