Let $V$ be a countable dimensional right vector space over $\mathbb Q$. $R=End(V_\mathbb Q)$, written on the left. In other words, the column-finite infinite matrices indexed by $\mathbb N$ over $\mathbb Q$.
Notes: Has exactly three ideals: the nontrivial one is the set of transformations with finite dimensional range.
Keywords endomorphism ring ring of functions
| Name | Measure | |
|---|---|---|
| cardinality | $\mathfrak c$ | |
| composition length | left: $\infty$ | right: $\infty$ |
| Krull dimension (classical) | 1 | |
| weak global dimension | 0 |
| Name | Description |
|---|---|
| Jacobson radical | $\{0\}$ |
| Left singular ideal | $\{0\}$ |
| Right singular ideal | $\{0\}$ |