Ring $R_{ 146 }$

Description:

Let $W = $ $R_{178}$. The field $F$ contains two maximal (linearly compact) valuation domains $V_1$ and $V_2$ with fields of fractions equal to $F$ and $V_1 + V_2 = F$. Let $S = V_1 \cap V_2$, and $M_i$ be the maximal ideals of $V_i$. Set $T = \{ (x,y) \in W: x \in S\}$ and $I = \{ (0,y) \in W: y \in M_1\}$; then $I$ is an ideal of $T$. The ring is $T/I$.

Notes: It is given as an example of a torch ring that is not a split null extension.

Keywords quotient ring ring of Witt vectors subring