Ring $R_{ 19 }$

Right-not-left Noetherian triangular ring


Triangular ring $\begin{bmatrix}\mathbb Z&\mathbb Q \\ 0&\mathbb Q\end{bmatrix}$.

Keywords triangular ring


  • T.-Y. Lam. A first course in noncommutative rings. (2013) @ p 20

  • = has the property
  • = does not have the property
  • = information not in database
Name Measure
cardinality $\aleph_0$
composition length left: $\infty$right: $\infty$
global dimension left: right: 1
Name Description
Jacobson radical $\begin{bmatrix}0&\mathbb Q\\0&0\end{bmatrix}$
Left singular ideal $\{0\}$
Left socle $\{0\}$
Right singular ideal $\{0\}$
Right socle $\begin{bmatrix}0&\mathbb Q\\0&\mathbb Q\end{bmatrix}$