S-unit
= S-unit
{c}
{title2=$u\in\mathcal O_{K,S}^{\times}$}
An S-unit in a <number field> $K$ is an element $u\in K^*$ whose valuations outside the finite set $S$ vanish. Equivalently, it is a unit of the ring of S-integers $\mathcal O_{K,S}$. The <S-unit group> is finitely generated by the <Dirichlet unit theorem> together with generators arising from the inverted primes.