Ring detail

Name: Right-not-left nonsingular ring

Description: Triangular ring $\begin{bmatrix}\mathbb Z&\mathbb Z/(2)\\ 0&\mathbb Z/(2)\end{bmatrix}$

Keywords triangular ring


  • T.-Y. Lam. Lectures on modules and rings. (2012) @ p 248

  • = has the property
  • = does not have the property
  • = information not in database
Name Measure
cardinality $\aleph_0$
composition length left: $\infty$right: $\infty$
Name Description
Jacobson radical $\begin{bmatrix}0&\mathbb Z/(2)\\0&0\end{bmatrix}$
Left socle $\begin{bmatrix}0&\mathbb Z/(2)\\0&0\end{bmatrix}$
Right socle $\begin{bmatrix}0&\mathbb Z/(2)\\0&\mathbb Z/(2)\end{bmatrix}$