Ring detail

Name: Chase's left-not-right semihereditary ring

Description: Let $S$ be von Neumann regular which has an ideal $I$ which is not a direct summand of $S_S$. Let $R$ be $S/I$. Form the triangular ring $T=\begin{bmatrix}R&R\\ 0& S\end{bmatrix}$. $T$ is the ring. For concreteness, we pick $S=\prod_{i=1}^\infty F_2$, and $I$ a maximal essential ideal.

Krull dimension: 0

Keywords quotient ring triangular ring

Reference(s):

• T.-Y. Lam. Lectures on modules and rings. (2012) @ pp 47-48