Let $\bar{\mathbb Q}$ be the algebraic closure of $\mathbb Q$ in $\mathbb C$.The required ring is $R=\bar{\mathbb Q}+X\mathbb C[[X]]$, a subring of the power series ring $\mathbb C[[X]]$.
Keywords algebraic closure power series ring subring
| Name | Measure | |
|---|---|---|
| Krull dimension (classical) | 1 |
| Name | Description |
|---|---|
| Idempotents | $\{0,1\}$ |
| Left singular ideal | $\{0\}$ |
| Left socle | $\{0\}$ |
| Nilpotents | $\{0\}$ |
| Right singular ideal | $\{0\}$ |
| Right socle | $\{0\}$ |
| Zero divisors | $\{0\}$ |