Category:Definitions/P-adic Integers

This category contains definitions related to P-adic Integers.
Related results can be found in Category:P-adic Integers.

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

An element $x \in \Q_p$ is called a $p$-adic integer if and only if $\norm x_p \le 1$.

The set of all $p$-adic integers is usually denoted $\Z_p$.

Thus:

$\Z_p = \set {x \in \Q_p: \norm x_p \le 1}$