Ring $R_{ 78 }$

Page's left-not-right FPF ring


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


  • (Citation needed)

  • Legend
    • = has the property
    • = does not have the property
    • = information not in database
    Name Measure
    composition length left: $\infty$right: $\infty$
    Name Description
    Left singular ideal $\begin{bmatrix}0&S\\0&0\end{bmatrix}$
    Right singular ideal $\{0\}$