Two generators for an ideal in a Dedekind domain
= Two generators for an ideal in a Dedekind domain
Every <ideal> of a <Dedekind domain> is generated by at most two elements. Given a nonzero <ideal> $I$ and any prescribed nonzero $a\in I$, the <Chinese remainder theorem> supplies $b\in I$ with $v_P((b))=v_P(I)$ at every <prime ideal> dividing $(a)$. The <prime-ideal valuation in a Dedekind domain> then gives $I=(a,b)$.