Let $Q$ be a commutative, non-Artinian, self-injective von Neumann regular ring: we choose $Q=R_{57}$. Let $M$ be a maximal ideal which is essential as a submodule of $Q$. Let $S=Q/M$, and $D=End_Q(S)$. The ring is $R=\begin{bmatrix}Q&S\\0&D\end{bmatrix}$
Notes: Left singular ideal is the subset of strictly upper triangular matrices.
Keywords triangular ring
| Name | Measure | |
|---|---|---|
| composition length | left: $\infty$ | right: $\infty$ |
| Name | Description |
|---|---|
| Left singular ideal | $\begin{bmatrix}0&S\\0&0\end{bmatrix}$ |
| Right singular ideal | $\{0\}$ |