The adelic fields in examples 2.49 and 2.50 will be called global fields. For a finite subset $S\subset\mathfrak{M}_{\mathbb{K}}$ containing the Archimedean places, we consider the Noetherian ring $\mathbb{K}^{\circ}_{S}=\{\alpha\in\mathbb{K}\,|\,|\alpha|_{v}\leq 1,\forall v\notin S\}$.