Multiplicative algebraic group
= Multiplicative algebraic group
{title2=$\mathbb G_m$}
The multiplicative <algebraic group> has $\mathbb G_m(K)=K^{\times}$, with multiplication as its <group operation>. Its coordinate ring is $K[z,z^{-1}]$. The <formal multiplicative group> describes its law near the identity $z=1$.