# Ring detail

## Name: Page's left-not-right FPF ring

Description: Let $Q$ be a commutative, non-Artinian, self-injective von Neumann regular ring. Let $M$ be a maximal left ideal which is essential in $Q$. Let $S=Q/M$, and $D=End_Q(S)$. The ring is $R=\begin{bmatrix}Q&S\\0&D\end{bmatrix}$

Notes: Right singular ideal is the subset of upper-triangular matrices.

Krull dimension: (unknown)

Keywords triangular ring

Reference(s):

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