Let $D=k[[x]]$ for a countably infinite field $k$ and let $Q$ be the field of fractions of $D$. Set $V=Q/D$. The ring is the trivial extension $T(D, V)$
Keywords power series ring trivial extension
| Name | Measure | |
|---|---|---|
| cardinality | $\mathfrak c$ | |
| composition length | left: $\infty$ | right: $\infty$ |
| Krull dimension (classical) | 1 |
| Name | Description |
|---|---|
| Idempotents | $\{0,1\}$ |