Ring $R_{ 97 }$

Description:

Let $\mathbb Z_{(p)}$ be the localization of the integers at a prime $p$, and $\mathbb Z_{p^\infty}$ be the Prüfer $p$ group, and $\mathbb Z_p=End(\mathbb Z_{p^\infty})$ be the $p$-adic integers. Then $R$ is the ring $\begin{bmatrix}\mathbb Z_{(p)}& \mathbb Z_{p^\infty}\\0&\mathbb Z_p \end{bmatrix}$

Notes: 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