The ring of $n \times n$ matrices with entries from $\mathbb Q$, and $n$ a natural number greater than $1$
Keywords matrix ring
| Name | Measure | |
|---|---|---|
| cardinality | $\aleph_0$ | |
| composition length | left: $n$ | right: $n$ |
| global dimension | left: 0 | right: 0 |
| Krull dimension (classical) | 0 | |
| uniform dimension | left: $n$ | right: $n$ |
| weak global dimension | 0 |
| Name | Description |
|---|---|
| Jacobson radical | $\{0\}$ |
| Left singular ideal | $\{0\}$ |
| Left socle | $R$ |
| Right singular ideal | $\{0\}$ |
| Right socle | $R$ |