Let $k$ be a field of characteristic $p>0$ such that $[k:k^p]=\infty$. Let $A=k[[x]]$. The required ring is the subring $R$ of elements of $A$ of elements of the form $\sum_0^\infty k_ix^i$ satisfying $[k^p(k_0, k_1,k_2,\ldots): k^p] <\infty$.
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 | $\{0\}$ |