Let $s$ be a field endomorphism from a countably infinite field $k$ to $k$ such that the image $L$ has infinite index in $k$. Define multiplication on $R=k\times k$ by $(x,y)(x',y')=(xx',s(x)y'+yx')$. $R$ is the ring
Keywords triangular ring
| Name | Measure | |
|---|---|---|
| cardinality | $\aleph_0$ | |
| composition length | left: $\infty$ | right: |
| Krull dimension (classical) | 0 |
| Name | Description |
|---|---|
| Idempotents | $\{0,1\}$ |