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This book is concerned with the research conducted in the late 1970s and early 1980s in the theory of commutative Neotherian rings. It consists of articles by invited speakers at the Symposium of Commutative Algebra held at the University of Durham in July 1981; these articles are all based on lectures delivered at the Symposium. The purpose of this book is to provide a record of at least some aspects of the Symposium, which several of the world leaders in the field attended. Several articles are included which provide surveys, incorporating historical perspective, details of progress made and…mehr
This book is concerned with the research conducted in the late 1970s and early 1980s in the theory of commutative Neotherian rings. It consists of articles by invited speakers at the Symposium of Commutative Algebra held at the University of Durham in July 1981; these articles are all based on lectures delivered at the Symposium. The purpose of this book is to provide a record of at least some aspects of the Symposium, which several of the world leaders in the field attended. Several articles are included which provide surveys, incorporating historical perspective, details of progress made and indications of possible future lines of investigation. The book will be of interest to scholars of commutative and local algebra.
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Preface; Addresses of contributors; List of participants; Part I. The Local Homological Conjectures, Big Cohen-Macaulay Modules, and Related Topics: 1. The syzygy problem: a new proof and historical perspective E. G. Evans and Phillip Griffith; 2. The theory of homological dimensions of complexes Hans-Bjørn Foxby; 3. Complexes of injective modules Hans-Bjørn Foxby; 4. The local homological conjectures Melvin Hochster; 5. The rank of a module G. Horrocks; 6. Modules of generalized fractions and balanced big Cohen-Macaulay modules R. Y. Sharp and H. Zakeri; 7. Sur la théorie des complexes parfaits L. Szpiro; Part II. Determinantal Ideals, Finite Free Resolutions, and Related Topics: 8. Some exact complexes and filtrations related to certain special Young diagrams Kaan Ankin and David A. Buschsbaum; 9. The canonical module of a determinantal ring Winfried Bruns; 10. The MacRae invariant Hans-Bjørn Foxby; 11. Finite free resolutions and some basic concepts of commutative algebra D. G. Northcott; Part III. Multiplicity Theory, Hilbert and Poincaré Series, Associated Graded Rings, and Related Topics: 12. Blowing-up of Buschsbaum rings Shiro Goto; 13. Necessary conditions for an analytical algebra to be strict J. Herzog; 14. Multiplicities, Hilbert functions and degree functions D. Rees; 15. Finiteness conditions in commutative algebra and solution of a problem of Vasconcelos Jan-Erik Roos; 16. On the use of graded Lie algebras in the theory of local tings Jan-Erik Roos; 17. Reductions, local cohomology and Hilbert functions of local rings Judith D. Sally; Further problems.
Preface; Addresses of contributors; List of participants; Part I. The Local Homological Conjectures, Big Cohen-Macaulay Modules, and Related Topics: 1. The syzygy problem: a new proof and historical perspective E. G. Evans and Phillip Griffith; 2. The theory of homological dimensions of complexes Hans-Bjørn Foxby; 3. Complexes of injective modules Hans-Bjørn Foxby; 4. The local homological conjectures Melvin Hochster; 5. The rank of a module G. Horrocks; 6. Modules of generalized fractions and balanced big Cohen-Macaulay modules R. Y. Sharp and H. Zakeri; 7. Sur la théorie des complexes parfaits L. Szpiro; Part II. Determinantal Ideals, Finite Free Resolutions, and Related Topics: 8. Some exact complexes and filtrations related to certain special Young diagrams Kaan Ankin and David A. Buschsbaum; 9. The canonical module of a determinantal ring Winfried Bruns; 10. The MacRae invariant Hans-Bjørn Foxby; 11. Finite free resolutions and some basic concepts of commutative algebra D. G. Northcott; Part III. Multiplicity Theory, Hilbert and Poincaré Series, Associated Graded Rings, and Related Topics: 12. Blowing-up of Buschsbaum rings Shiro Goto; 13. Necessary conditions for an analytical algebra to be strict J. Herzog; 14. Multiplicities, Hilbert functions and degree functions D. Rees; 15. Finiteness conditions in commutative algebra and solution of a problem of Vasconcelos Jan-Erik Roos; 16. On the use of graded Lie algebras in the theory of local tings Jan-Erik Roos; 17. Reductions, local cohomology and Hilbert functions of local rings Judith D. Sally; Further problems.
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