Definition:P-adic Integer

Definition
Let $\norm {\,\cdot\,}_p$ be the $p$-adic norm on the $p$-adic numbers $\Q_p$ for some prime $p$.

The $p$-adic integers, denoted $\Z_p$, is the valuation ring induced by $\norm {\,\cdot\,}_p$, that is:
 * $\Z_p = \set{x \in \Q_p : \norm{x}_p \le 1}$

Notation
The notation $\Z_p$ is also used for the ring of integers module $p$ where $p$ is a prime number. On the context of any page where $\Z_p$ appears will define what is referred to by $\Z_p$.