= Spectrum map for the complexification of a real polynomial ring
{title2=$\operatorname{Spec}\mathbb C[x]\to\operatorname{Spec}\mathbb R[x]$}
Contraction sends the zero <prime ideal> to zero. A complex closed point $(x-z)$ contracts to $(x-z)$ when $z$ is real, and to $((x-\operatorname{Re}z)^2+(\operatorname{Im}z)^2)$ otherwise. Thus the map on the <spectrum of a commutative ring> is surjective and identifies each nonreal conjugate pair. Both spectra have only finite proper <Zariski-closed sets>, so this is also the topological quotient by complex conjugation.
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