 Prime-filter locale of a commutative ring

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.