Definition:P-adic Unit

Definition
Let $p$ be a prime number.

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

Let $\Z_p$ denote the $p$-adic integers.

The set of $p$-adic units, denoted $\Z_p^\times$, is the set of invertible elements of $\Z_p$.

Also see

 * P-adic Unit has Norm Equal to One where it is shown that the $p$-adic units is:
 * $\Z_p^\times = \set {x \in \Q_p: \norm x_p = 1}$


 * P-adic Expansion of P-adic Unit where it is shown that the $p$-adic units is:
 * $\Z_p^\times = \set {\ds \sum_{n \mathop = 0}^\infty a_n p^n \in \Q_p: a_0 \ne 0}$