TY  - BOOK
AU  - Heinzer,William J.
AU  - Huneke,Craig L.
AU  - Sally,Judith D.
TI  - Commutative Algebra: Syzygies, Multiplicities, and Birational Algebra
T2  - Contemporary Mathematics Series
SN  - 9780821877500
AV  - QA251.3 .C657 1992 
U1  - 512/.24 
PY  - 1994///
CY  - Providence
PB  - American Mathematical Society
KW  - Commutative algebra-Congresses
KW  - Electronic books
N1  - 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 algebras -- 5. 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 law -- Proximity 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 ideals; Artin-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
N2  - 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 commutative algebra and interactions with such areas as algebraic geometry, representation theory, and combinatorics. The major themes of the conference were tight closure Hilbert functions, birational algebra, free resolutions and the homological conjectures, Rees algebras, and local cohomology. With contributions by several leading experts in the field, this volume provides an excellent survey of current research in commutative algebra
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ER  -