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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.
List of contents
Representations, Resolutions and Intertwining Numbers.- Cohen-Macaulay Modules for Graded Cohen-Macaulay Rings and Their Completions.- Homological Asymptotics of Modules Over Local Rings.- On Ulrich-Modules Over Hypersurface Rings.- Differential Structure of Étale Extensions of Polynomial Algebras.- Additions to the Theory of Algebras with Straightening Law.- Syzygies and Homological Conjectures.- Remarks on Points in a Projective Space.- Rank Varieties of Matrices.- Order Ideals.- A Characterization of F-Regularity in Terms of F-Purity.- Surface Singularities of Finite Buchsbaum-Representation Type.- Some Transcendence Degree Questions.- Exceptional Prime Divisors Of Two-Dimensional Local Domains.- Tight Closure.- Complete Ideals in Two-Dimensional Regular Local Rings.- Powers Of Licci Ideals.- The Hilbert Function of a Gorenstein Artin Algebra.- On Unramifying Transcendence Base.- A Survey of Problems and Results on the Number of Defining Equations.- Integrally Closed Projectively Equivalent Ideals.- Izumi's Theorem.- Intersection Theorems.- One-Fibered Ideals.- A Method for the Study of Artinian Modules, With an Application to Asymptotic Behavior.- Symmetric Algebras and Factoriality.- Noetherian Rings of Bounded Representation Type.
Summary
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.
