The required ring is the subset of $p(X)\in \mathbb Q[X]$ for which $p(z)\in\mathbb Z$ for every $z\in\mathbb Z$.
Notes: Not Noetherian, but Gilmer and Smith proved f.g. ideals are all generated by at most 2 elements. It is countable, but its prime spectrum is not. None of the nonzero prime ideals are finitely generated
Keywords polynomial ring subring
(Nothing was retrieved.)
| 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 | $\{0\}$ |