[[!redirects Sandbox > history]] [[!redirects Sandbox]] < [[nlab:Sandbox]] | | Integers | Polynomials of integrally closed discrete field | Polynomials of Cantor complex numbers | |-|---------|------------------|------------------| | Base ring | $\mathbb{Z}$ | $\overline{F}[\epsilon]$ | $\mathbb{C}_C[\epsilon]$ | | Field at prime | $\mathbb{Z}/p$ | $\overline{F}[\epsilon]/(\epsilon - x) \cong \overline{F}$ | $\mathbb{C}_C[\epsilon]/(\epsilon - z) \cong \mathbb{C}_C$ | | Weil algebra at prime power | $\mathbb{Z}/p^n$ | $\overline{F}[\epsilon]/(\epsilon - x)^n$ | $\mathbb{C}_C[\epsilon]/(\epsilon - z)^n$ | | Topological completion | $\mathbb{Z}_{p}$ | $\overline{F}[[\epsilon - x]]$ | $\mathbb{C}_C[[\epsilon - z]]$ | | | Integers | Polynomials of discrete prefield | |-|---------|------------------| | Base ring | $\mathbb{Z}$ | $\overline{F}[\epsilon]$ | | Prefield ring at square-free number | $\mathbb{Z}/m$ | $\overline{F}[\epsilon]/(\epsilon - x) \cong \overline{F}$ | | pre-Weil algebra at power of square-free number | $\mathbb{Z}/m^n$ | $\overline{F}[\epsilon]/(\epsilon - x)^n$ | | Topological completion | $\mathbb{Z}_{m}$ | $\overline{F}[[\epsilon - x]]$ | Shapes as types, to define extension types... category: redirected to nlab