Let $A=$ $R_{69}$, and $k=A/(2)$, and $\widehat{A}$ be the $(2)$-adic completion of $A$. The ring in question is a localization of a ring between $A$ and $\widehat{A}$. (See link for details, $C_M$ in the article.)
Notes: Details in https://arxiv.org/pdf/alg-geom/9503017.pdf
Keywords completion localization subring
| Name | Measure | |
|---|---|---|
| Krull dimension (classical) | 1 |
| Name | Description |
|---|---|
| Idempotents | $\{0,1\}$ |
| Left singular ideal | $\{0\}$ |
| Left socle | $\{0\}$ |
| Nilpotents | $\{0\}$ |
| Right singular ideal | $\{0\}$ |
| Right socle | $\{0\}$ |
| Zero divisors | $\{0\}$ |