Global unit of a number field
= Global unit of a number field
{title2=$E_K=\mathcal O_K^\times$}
= Global unit
{synonym}
A <global unit> and its inverse are algebraic integers in the number <field>. Equivalently its valuation is zero at every nonarchimedean prime. <Global units> embed in <local unit> groups; their p-adic closures can be smaller than the full local groups. This discrepancy is measured by the <class-field unit sequence>.