Ring $R_{ 39 }$

Chase's left-not-right semihereditary ring


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.

Keywords quotient ring triangular ring


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

  • = has the property
  • = does not have the property
  • = information not in database
Name Measure
cardinality $\mathfrak c$
composition length left: $\infty$right: $\infty$
Krull dimension (classical) 0
Name Description
Left singular ideal $\{0\}$