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

Symmetric properties

Asymmetric properties

Legend

- = 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 singular ideal | $\{0\}$ |

Right socle | $\begin{bmatrix}0&\mathbb Z/(2)\\0&\mathbb Z/(2)\end{bmatrix}$ |