Prime-filter locale of a commutative ring
= Prime-filter locale of a commutative ring
{title2=$X_R$}
For a <commutative ring> $R$, this <locale> is presented by basic opens $U_r$ recording membership in a multiplicatively closed prime filter. Products give intersections. A ring map induces a <locale> map in the opposite direction. The basic opens satisfy $U_r\vee U_s=1$ exactly when $(r,s)=R$, making unit-ideal calculations a substitute for choosing prime ideals.