## Progress in Commutative Algebra 1: Combinatorics and HomologyChristopher Francisco, Lee C. Klingler, Sean Sather-Wagstaff, Janet C. Vassilev This is the first of two volumes of a state-of-the-art survey article collection which emanates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University meeting. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. The current trends in two of the most active areas of commutative algebra are presented: non-noetherian rings (factorization, ideal theory, integrality), advances from the homological study of noetherian rings (the local theory, graded situation and its interactions with combinatorics and geometry). This fist volume concentrates on combinatorics and homology. |

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### Contents

1 | |

the Twofold Way | 55 |

Algebraic and Combinatorial Properties | 85 |

Three Simplicial Resolutions | 127 |

A Minimal Poset Resolution of Stable Ideals | 143 |

Subsets of Complete Intersections and the EGH Conjecture | 167 |

The Homological Conjectures | 199 |

The Compatibility Independence and Linear Growth Properties | 231 |

a Homological Perspective | 271 |

Scenes from Categorical Geometry | 293 |

### Other editions - View all

Progress in Commutative Algebra 2 : Closures, Finiteness and Factorization No preview available - 2012 |