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

Known Properties

Legend

- = has the property
- = does not have the property
- = information not in database

(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 | $\{0\}$ |