Ebook: Commutative Algebra: Proceedings of a Microprogram Held June 15–July 2, 1987

During late June and early July of 1987 a three week program (dubbed "microprogram") in Commutative Algebra was held at the Mathematical Sciences Research Institute at Berkeley. The intent of the microprogram was to survey recent major results and current trends in the theory of commutative rings, especially commutative Noetherian rings. There was enthusiastic international participation. The papers in this volume, some of which are expository, some strictly research, and some a combination, reflect the intent of the program. They give a cross-section of what is happening now in this area. Nearly all of the manuscripts were solicited from the speakers at the conference, and in most instances the manuscript is based on the conference lecture. The editors hope that they will be of interest and of use both to experts and neophytes in the field. The editors would like to express their appreciation to the director of MSRI, Professor Irving Kaplansky, who first suggested the possibility of such a conference and made the task of organization painless. We would also like to thank the IVISRI staff who were unfailingly efficient, pleasant, and helpful during the meeting, and the manager of MSRI, Arlene Baxter, for her help with this volume. Finally we would like to express our appreciation to David Mostardi who did much of the typing and put the electronic pieces together.

---

The papers in this volume, some of which are expository, some strictly research, and some a combination, reflect the intent of the program. They give a cross-section of what is happening now in this area. Nearly all of the manuscripts were solicited from speakers at the conference, and in most instances the manuscript is based on the conference lecture. The editors hope that they will be of interest and of use both to experts and neophytes in the field.

---

The papers in this volume, some of which are expository, some strictly research, and some a combination, reflect the intent of the program. They give a cross-section of what is happening now in this area. Nearly all of the manuscripts were solicited from speakers at the conference, and in most instances the manuscript is based on the conference lecture. The editors hope that they will be of interest and of use both to experts and neophytes in the field.
Content:
Front Matter....Pages i-x
Representations, Resolutions and Intertwining Numbers....Pages 1-19
Cohen-Macaulay Modules for Graded Cohen-Macaulay Rings and their Completions....Pages 21-31
Homological Asymptotics of Modules over Local Rings....Pages 33-62
On Ulrich-Modules over Hypersurface Rings....Pages 63-68
Differential Structure of ?tale Extensions of Polynomial Algebras....Pages 69-109
Additions to the Theory of Algebras with Straightening Law....Pages 111-138
Syzygies and Homological Conjectures....Pages 139-156
Remarks on Points in a Projective Space....Pages 157-172
Rank Varieties of Matrices....Pages 173-212
Order Ideals....Pages 213-225
A Characterization of F-Regularity in Terms of F-Purity....Pages 227-245
Surface Singularities of Finite Buchsbaum-Representation Type....Pages 247-263
Some Transcendence Degree Questions....Pages 265-277
Exceptional Prime Divisors of Two-dimensional Local Domains....Pages 279-304
Tight Closure....Pages 305-324
Complete Ideals in Two-Dimensional Regular Local Rings....Pages 325-338
Powers of Licci Ideals....Pages 339-346
The Hilbert Function of a Gorenstein Artin Algebra....Pages 347-364
On Unramifying Transcendence Base....Pages 365-373
A Survey of Problems and Results on the Number of Defining Equations....Pages 375-390
Integrally Closed Projectively Equivalent Ideals....Pages 391-405
Izumi’s Theorem....Pages 407-416
Intersection Theorems....Pages 417-436
One-Fibered Ideals....Pages 437-442
A Method for the Study of Artinian Modules, With an Application to Asymptotic Behavior....Pages 443-465
Symmetric Algebras and Factoriality....Pages 467-496
Noetherian Rings of Bounded Representation Type....Pages 497-516

---

The papers in this volume, some of which are expository, some strictly research, and some a combination, reflect the intent of the program. They give a cross-section of what is happening now in this area. Nearly all of the manuscripts were solicited from speakers at the conference, and in most instances the manuscript is based on the conference lecture. The editors hope that they will be of interest and of use both to experts and neophytes in the field.
Content:
Front Matter....Pages i-x
Representations, Resolutions and Intertwining Numbers....Pages 1-19
Cohen-Macaulay Modules for Graded Cohen-Macaulay Rings and their Completions....Pages 21-31
Homological Asymptotics of Modules over Local Rings....Pages 33-62
On Ulrich-Modules over Hypersurface Rings....Pages 63-68
Differential Structure of ?tale Extensions of Polynomial Algebras....Pages 69-109
Additions to the Theory of Algebras with Straightening Law....Pages 111-138
Syzygies and Homological Conjectures....Pages 139-156
Remarks on Points in a Projective Space....Pages 157-172
Rank Varieties of Matrices....Pages 173-212
Order Ideals....Pages 213-225
A Characterization of F-Regularity in Terms of F-Purity....Pages 227-245
Surface Singularities of Finite Buchsbaum-Representation Type....Pages 247-263
Some Transcendence Degree Questions....Pages 265-277
Exceptional Prime Divisors of Two-dimensional Local Domains....Pages 279-304
Tight Closure....Pages 305-324
Complete Ideals in Two-Dimensional Regular Local Rings....Pages 325-338
Powers of Licci Ideals....Pages 339-346
The Hilbert Function of a Gorenstein Artin Algebra....Pages 347-364
On Unramifying Transcendence Base....Pages 365-373
A Survey of Problems and Results on the Number of Defining Equations....Pages 375-390
Integrally Closed Projectively Equivalent Ideals....Pages 391-405
Izumi’s Theorem....Pages 407-416
Intersection Theorems....Pages 417-436
One-Fibered Ideals....Pages 437-442
A Method for the Study of Artinian Modules, With an Application to Asymptotic Behavior....Pages 443-465
Symmetric Algebras and Factoriality....Pages 467-496
Noetherian Rings of Bounded Representation Type....Pages 497-516
....