Choose a prime$p$ and an infinite degree field extension$K$ of a characteristic $p$ field $k$ such that $K^{p}\subseteq k$. Let the discrete valuation ring $R$ be the ring of formal power series over $K$ whose coefficients generate a finite extension of $k$.
Keywords power series ring subring
| Name | Measure | |
|---|---|---|
| global dimension | left: 1 | right: 1 |
| 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 | $\{0\}$ |