Let $G$ be the subgroup of "eventually constant" sequences in $\mathbb Z^\mathbb N$ (meaning except for finitely many positions, the positions are equal). $G$ is a lattice ordered group with the order $(z_n)\leq (z'_n)$ given by $z_i\leq z'_i$ for all $i\in \mathbb N$. The desired ring is the Jaffard-Ohm-Kaplansky construction that yields a Bezout domain with value group $G$.
Keywords Jaffard-Ohm-Kaplansky construction
(Nothing was retrieved.)
| Name | Description |
|---|---|
| Idempotents | $\{0,1\}$ |
| Left singular ideal | $\{0\}$ |
| Left socle | $\{0\}$ |
| Nilpotents | $\{0\}$ |
| Right singular ideal | $\{0\}$ |
| Right socle | $\{0\}$ |
| Zero divisors | $\{0\}$ |