Ring detail


Name: Right-not-left Noetherian triangular ring

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

Keywords triangular ring

Reference(s):

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



Legend
  • = 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 socle $\begin{bmatrix}0&0\\0&0\end{bmatrix}$
Right socle $\begin{bmatrix}0&\mathbb Q\\0&\mathbb Q\end{bmatrix}$