On an Euler product ring (Q1080470)

The author studies the completion \(\hat A=\prod_{{\mathfrak p}}A_{{\mathfrak p}}\) of the ring A of integers in some finite number field F. Using results from nonstandard number theory he proves that the space \(M(\hat A)\) of maximal ideals is Hausdorff compact and that the space \(\Omega(\hat A)\) of Kähler differentials does not vanish. Finally he mentions results on the analytic behaviour of special zeta functions being the product of infinitely, but not cofinitely many local Euler factors.