Let $\mathbb Z_{(2)}$ be the localization of the integers at $(2)$ ($R_{69}$), and $\mathbb Z_{2^\infty}$ be the Prüfer $2$ group, and $\mathbb Z_2=End(\mathbb Z_{2^\infty})$ ($M_{17}$) be the $2$-adic integers ($R_{84}$). Then $R$ is the ring $\begin{bmatrix}\mathbb Z_{(2)}& \mathbb Z_{2^\infty}\\0&\mathbb Z_2 \end{bmatrix}$

Notes: Puninski used any prime $p$, not just $2$. Krull dimension $1$, (probably Rentschler-Michler Krull dimension) The radical is the union of the singular ideals. It is its own classical quotient ring.

Keywords completion localization triangular ring

- G. Puninski. Serial rings. (2001) @ Example 9.15 p 120

Symmetric properties

Asymmetric properties

Legend

- = has the property
- = does not have the property
- = information not in database

Name | Measure | |
---|---|---|

cardinality | $\mathfrak c$ |

Name | Description |
---|---|

Right singular ideal | $\begin{bmatrix}p\mathbb Z_(p)&Z_{p_\infty}\end{bmatrix}$ |