Description: Let $S$ be the subset of infinite matrices over a countably infinite field $k$ which are nonzero only on finitely many entries above the diagonal. $R$ is the subring of the matrix ring generated by $S$ and the "infinite" identity matrix.

Keywords infinite matrix ring subring

Reference(s):

- T.-Y. Lam. A first course in noncommutative rings. (2013) @ pp 345-346

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 |
---|---|

Idempotents | $\{0,1\}$ |