p-adic unit (${\mathbb{Z}}_p^{\times }$)

A p-adic unit is an element of ${\mathbb{Z}}_p^{\times }$, equivalently a p-adic integer of valuation zero.

For a non-Archimedean local field $K$ with maximal ideal ${\mathfrak{m}}_K$, a principal unit is an element of $1+{\mathfrak{m}}_K$. The higher principal-unit groups are $1+{\mathfrak{m}}_K^n$.