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035 | ⊔ | ⊔ | ‡a(DBlue)diss 133408 |

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040 | ⊔ | ⊔ | ‡aMiU ‡cMiU |

042 | ⊔ | ⊔ | ‡adc |

100 | 1 | ⊔ | ‡aRebhuhn-Glanz, Rebecca. |

245 | 1 | 0 | ‡aClosure Operations that Induce Big Cohen-Macaulay Modules and Algebras, and Classification of Singularities ‡h[electronic resource]. |

260 | ⊔ | ⊔ | ‡c2016. |

502 | ⊔ | ⊔ | ‡aDissertation (Ph.D.)--University of Michigan. PhD |

504 | ⊔ | ⊔ | ‡aIncludes bibliographical references. |

520 | 3 | ⊔ | ‡aregular closure are not Dietz closures, and that all Dietz closures are contained in liftable integral closure. We give an additional axiom for a closure operation such that the existence of a Dietz closure satisfying this axiom is equivalent to the existence of a big Cohen-Macaulay algebra. We prove that many closure operations satisfy the Algebra Axiom, whether or not they are Dietz closures. We discuss the smallest big Cohen-Macaulay algebra closure on a given ring, and show that every Dietz closure satisfying the Algebra Axiom is contained in a big Cohen-Macaulay algebra closure. This leads to proofs that in rings of characteristic p > 0, every Dietz closure satisfying the Algebra Axiom is contained in tight closure, and there exist Dietz closures that do not satisfy the Algebra Axiom. |

520 | 3 | ⊔ | ‡aGeoffrey Dietz introduced a set of axioms for a closure operation on a complete local domain such that the existence of a closure operation satisfying these axioms is equivalent to the existence of a big Cohen-Macaulay module. These are called Dietz closures. In characteristic p > 0, tight closure and plus closure satisfy the axioms. In order to study these closures, we define module closures and discuss their properties. For many of these properties, there is a smallest closure operation satisfying the property. We discuss properties of big Cohen-Macaulay module closures, and prove that every Dietz closure is contained in a big Cohen-Macaulay module closure. Using this result, we show that under mild conditions, a ring R is regular if and only if all Dietz closures on R are trivial. We also show that solid closure in equal characteristic 0, integral closure, and |

538 | ⊔ | ⊔ | ‡aMode of access: Internet. |

650 | ⊔ | 4 | ‡aCommutative algebra. |

650 | ⊔ | 4 | ‡aCohen-macaulay module. |

650 | ⊔ | 4 | ‡aClosure operation. |

650 | ⊔ | 4 | ‡aTight closure. |

690 | ⊔ | 4 | ‡aMathematics. |

710 | 2 | ⊔ | ‡aUniversity of Michigan. ‡bLibrary. ‡bDeep Blue. |

899 | ⊔ | ⊔ | ‡a39015089730066 |

CID | ⊔ | ⊔ | ‡a102153809 |

DAT | 0 | ⊔ | ‡a20231111015347.0 ‡b20231111000000.0 |

DAT | 1 | ⊔ | ‡a20231112060855.0 ‡b2023-11-12T14:46:37Z |

DAT | 2 | ⊔ | ‡a2017-08-22T18:00:03Z |

CAT | ⊔ | ⊔ | ‡aSDR-MIU ‡cmiu ‡dALMA ‡lprepare.pl-004-008 |

FMT | ⊔ | ⊔ | ‡aBK |

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974 | ⊔ | ⊔ | ‡bMIU ‡cMIU ‡d20231112 ‡slit-dlps-dc ‡umdp.39015089730066 ‡y2016 ‡ric ‡qbib ‡tUS bib date1 >= 1929 |