Commutative Algebra.

Commutative Algebra.

This volume contains refereed papers on themes explored at the AMS-IMS-SIAM Summer Research Conference, Commutative Algebra: Syzygies, Multiplicities, and Birational Algebra, held at Mount Holyoke College in 1992. The conference featured a series of one-hour invited lectures on recent advances in co...

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Bibliographic Details
Main Author: Heinzer, William J.
Other Authors: Huneke, Craig L., Sally, Judith D.
Format: eBook
Language:English
Published: Providence : American Mathematical Society, 1994.
Series:Contemporary Mathematics Ser.
Subjects:
Commutative algebra > Congresses.
Commutative algebra
Conference papers and proceedings
Online Access:Click for online access
Table of Contents:
  • Intro; Contents; Preface; Grothendieck""s localization problem; A simple proof of Grothendieck's theorem on the parafactoriality of local rings; Resolutions with a given Hilbert function; Complete ideals in algebra and geometry; On the Cohen-Macaulay type of perfect ideals; On the Gorensteinness of graded rings associated to ideals of analytic deviation one; Prime ideals in birational extensions of polynomial rings; On the index of a homogeneous Gorenstein ring; Solid closure; 1. Introduction; 2. Solid modules and solid algebras; 3. Formally solid modules and algebras.
  • 4. Generic forcing algebras5. Solid closure; 6. Minimal solid algebras; 7. S-regular rings; 8. Comparison with tight closure in characteristic p; 9. A formal power series criterion; 10. Shadow homology; 11. Big Cohen-Macaulay algebras and tight closure in equal characteristic zero; 12. The case of dimension two; 13. Regular rings revisited; 14. Questions; Tight closure in equal characteristic, big Cohen-Macaulay algebras, and solid closure; Indecomposable canonical modules and connectedness; Multiplicities in graded rings I: The general theory.
  • Pfaffian identities, with applications to free resolutions, DG-algebras, and algebras with straightening lawProximity inequalities for complete ideals in two-dimensional regular local rings; 0. Introduction; 1. Preliminaries; 2. Proximity inequalities; 3. Unique factorization; 4. Simple complete ideals; 5. Valuations and proximity; Cohomological annihilators and Castelnuovo-Mumford regularity; Local-global principle for annihilation of local cohomology; Multiplicities and Chern classes; A computation of local cohomology; Algebra structures for graded free resolutions.
  • Primary decompositions of powers of idealsArtin-Nagata properties and reductions of ideals; Hilbert functions, analytic spread, and Koszul homology; Infinite cyclic covers of strongly F-regular rings; Torsion in Picard groups of affine rings.

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