dc.contributor.author | Badawi, Ayman | |

dc.contributor.author | Jaballah, Ali | |

dc.date.accessioned | 2018-02-28T05:20:10Z | |

dc.date.available | 2018-02-28T05:20:10Z | |

dc.date.issued | 2008 | |

dc.identifier.citation | Badawi, A. (2008). Some finiteness conditions on the set of overrings of a phi-ring. Houston journal of mathematics, 34(2), 397-408. | en_US |

dc.identifier.issn | 0362-1588 | |

dc.identifier.uri | http://hdl.handle.net/11073/9225 | |

dc.description.abstract | Let H = {R | R is a commutative ring and Nil(R) is a divided prime ideal of R}. For a ring R in H with total quotient ring T(R), Let phi be the natural ring homomorphism from T(R) into R_Nil(R). An integral domain R is said to be an FC-domain (in the sense of Gilmer) if each chain of distinct overrings of R is finite, and R is called an FO-domain if R has finitely many overrings. A ring R is called an FC-ring if each chain of distinct overrings of R is finite, and R is said to be an FO-ring if R has finitely many overrings. A ring R in H is said to be a phi-FC-ring if phi(R) is an FC-ring, and R is called a phi-FO-ring if phi(R) is an FO-ring. In this paper, we show that the theory of phi-FC-rings and phi-FO-rings resembles that of FC-domains and FO-domains. | en_US |

dc.language.iso | en_US | en_US |

dc.publisher | University of Houston | en_US |

dc.relation.uri | http://www.math.uh.edu/~hjm/Vol34-2.html | |

dc.title | Some finiteness conditions on the set of overrings of a phi-ring | en_US |

dc.type | Article | en_US |

dc.type | Published version | en_US |

dc.type | Peer-Reviewed | en_US |