The ring of integers $\mathbb Z=\{...-3, -2, -1, 0, 1, 2, 3,...\}$ OR equivalence relation on $\mathbb N\times \mathbb N$ given by $(a,b)\sim(c,d)$ iff $a-b=c-d$
Keywords equivalence relation
| Name | Measure | |
|---|---|---|
| cardinality | $\aleph_0$ | |
| composition length | left: $\infty$ | right: $\infty$ |
| global dimension | left: 1 | right: 1 |
| Krull dimension (classical) | 1 | |
| weak global dimension | 1 |
| Name | Description |
|---|---|
| Idempotents | $\{0,1\}$ |
| Jacobson radical | $\{0\}$ |
| Left singular ideal | $\{0\}$ |
| Left socle | $\{0\}$ |
| Nilpotents | $\{0\}$ |
| Right singular ideal | $\{0\}$ |
| Right socle | $\{0\}$ |
| Units | $\{-1, 1\}$ |
| Zero divisors | $\{0\}$ |