## Abstract

Among other results, we prove the following: (1) A locally Archimedean stable domain satisfies accp. (2) A stable domain R is Archimedean if and only if every nonunit of R belongs to a height-one prime ideal of the integral closure R0 of R in its quotient field (this result is related to Ohm's theorem for Prufer domains). (3) An Archimedean stable domain R is one-dimensional if and only if R0 is equidimensional (generally, an Archimedean stable local domain is not necessarily one-dimensional). (4) An Archimedean finitely stable semilocal domain with stable maximal ideals is locally Archimedean, but generally, neither Archimedean stable domains, nor Archimedean semilocal domains are necessarily locally Archimedean.

Original language | English |
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Pages (from-to) | 179-198 |

Number of pages | 20 |

Journal | Journal of Commutative Algebra |

Volume | 12 |

Issue number | 2 |

DOIs | |

State | Published - 1 Jun 2020 |

### Bibliographical note

Publisher Copyright:© Rocky Mountain Mathematics Consortium.

## Keywords

- Accp
- Archimedean domain
- Completely integrally closed
- Finite character
- Finitely stable
- Locally archimedean
- Mori domain
- Stable ideal

## ASJC Scopus subject areas

- Algebra and Number Theory