The Henselization of $\Bbb Z_{(2)}$ is isomorphic to the subring of its completion (the 2-adic integers $\Bbb Z_{2}$) whose elements are roots of separable polynomials with coefficients in $\Bbb Z_{(2)}$.
Keywords Henselization completion subring
| Name | Measure | |
|---|---|---|
| cardinality | $\aleph_0$ | |
| 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 | $\{0\}$ |