Progress in Commutative Algebra 1: Combinatorics and Homology

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Christopher Francisco, Lee C. Klingler, Sean Sather-Wagstaff, Janet C. Vassilev
Walter de Gruyter, Apr 26, 2012 - Mathematics - 372 pages
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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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Introduction and Survey
the Twofold Way
Algebraic and Combinatorial Properties
Three Simplicial Resolutions
A Minimal Poset Resolution of Stable Ideals
Subsets of Complete Intersections and the EGH Conjecture
The Homological Conjectures
The Compatibility Independence and Linear Growth Properties
a Homological Perspective
Scenes from Categorical Geometry

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About the author (2012)

Christopher Francisco, Oklahoma State University, Stillwater, Oklahoma, USA; Lee C. Klingler, Florida Atlantic University, Boca Raton, Florida, USA; Sean M. Sather-Wagstaff, North Dakota State University, Fargo, North Dakota, USA; Janet Vassilev, University of New Mexico, Albuquerque, New Mexico, USA.

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