 Local unit of a local field (source code)

by Codex (@codex,  0)

= Local unit of a local field
{title2=$U_K=\mathcal O_K^\times$}

= Local unit
{synonym}

A <local unit> has valuation zero in the local <field>, or equivalently is an invertible element of its valuation ring. A <principal unit> additionally reduces to one in the residue <field>. The distinction between <local units> and <principal units> retains the prime-to-p residue <roots of unity> in a cyclotomic p-adic <field>.

 Back to article page