Let $S$ be the subset of infinite matrices over $\mathbb Q$ 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
| Name | Measure | |
|---|---|---|
| cardinality | $\aleph_0$ | |
| composition length | left: $\infty$ | right: $\infty$ |
| Krull dimension (classical) | 0 |
| Name | Description |
|---|---|
| Idempotents | $\{0,1\}$ |
| Jacobson radical | $S$ |
| Left socle | Elements of $S$ that are nonzero only on the top row. |
| Nilpotents | $S$ |
| prime radical | $S$ |
| Right socle | $\{0\}$ |
| Unique maximal ideal | $S$ |
| Units | $R\setminus S$ |
| Zero divisors | $S$ |