Title | **Syzygy Theorems via comparison of order ideals on a hypersurface** |

Author(s) | Phillip Griffith, Alexandra Seceleanu |

Type | Article in Journal |

Abstract | We introduce a weak order ideal property that suffices for establishing the Evans–Griffith Syzygy Theorem. We study this weak order ideal property in settings that allow for comparison between homological algebra over a local ring R versus a hypersurface ring R ̄ = R / ( x n ) . Consequently we solve some relevant cases of the Evans–Griffith syzygy conjecture over local rings of unramified mixed characteristic p , with the case of syzygies of prime ideals of Cohen–Macaulay local rings of unramified mixed characteristic being noted. We reduce the remaining considerations to modules annihilated by p s , s > 0 , that have finite projective dimension over a hypersurface ring. |

ISSN | 0022-4049 |

URL |
http://www.sciencedirect.com/science/article/pii/S0022404911001733 |

Language | English |

Journal | Journal of Pure and Applied Algebra |

Volume | 216 |

Number | 2 |

Pages | 468 - 479 |

Year | 2012 |

Edition | 0 |

Translation |
No |

Refereed |
No |