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Author : Donna Jean Glassbrenner
Publisher :
ISBN 13 :
Total Pages : 162 pages
Book Rating : 4.3/5 (91 download)
Download or read book Invariant Rings of Group Actions, Determinantal Rings, and Tight Closure written by Donna Jean Glassbrenner and published by . This book was released on 1992 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Craig Huneke
Publisher : American Mathematical Soc.
ISBN 13 : 082180412X
Total Pages : 152 pages
Book Rating : 4.8/5 (218 download)
Download or read book Tight Closure and Its Applications written by Craig Huneke and published by American Mathematical Soc.. This book was released on 1996 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with the theory of tight closure and its applications. The contents are based on ten talks given at a CBMS conference held at North Dakota State University in June 1995.
Author : J. Elias
Publisher : Springer Science & Business Media
ISBN 13 : 9783764359515
Total Pages : 424 pages
Book Rating : 4.3/5 (595 download)
Download or read book Six Lectures on Commutative Algebra written by J. Elias and published by Springer Science & Business Media. This book was released on 1998-06-16 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interest in commutative algebra has surged over the past decades. In order to survey and highlight recent developments in this rapidly expanding field, the Centre de Recerca Matematica in Bellaterra organized a ten-days Summer School on Commutative Algebra in 1996. Lectures were presented by six high-level specialists, L. Avramov (Purdue), M.K. Green (UCLA), C. Huneke (Purdue), P. Schenzel (Halle), G. Valla (Genova) and W.V. Vasconcelos (Rutgers), providing a fresh and extensive account of the results, techniques and problems of some of the most active areas of research. The present volume is a synthesis of the lectures given by these authors. Research workers as well as graduate students in commutative algebra and nearby areas will find a useful overview of the field and recent developments in it. Reviews "All six articles are at a very high level; they provide a thorough survey of results and methods in their subject areas, illustrated with algebraic or geometric examples." - Acta Scientiarum Mathematicarum Avramov lecture: "... it contains all the major results [on infinite free resolutions], it explains carefully all the different techniques that apply, it provides complete proofs (...). This will be extremely helpful for the novice as well as the experienced." - Mathematical reviews Huneke lecture: "The topic is tight closure, a theory developed by M. Hochster and the author which has in a short time proved to be a useful and powerful tool. (...) The paper is extremely well organized, written, and motivated." - Zentralblatt MATH Schenzel lecture: "... this paper is an excellent introduction to applications of local cohomology." - Zentralblatt MATH Valla lecture: "... since he is an acknowledged expert on Hilbert functions and since his interest has been so broad, he has done a superb job in giving the readers a lively picture of the theory." - Mathematical reviews Vasconcelos lecture: "This is a very useful survey on invariants of modules over noetherian rings, relations between them, and how to compute them." - Zentralblatt MATH
Author : William J. Heinzer
Publisher : American Mathematical Soc.
ISBN 13 : 0821851888
Total Pages : 456 pages
Book Rating : 4.8/5 (218 download)
Download or read book Commutative Algebra: Syzygies, Multiplicities, and Birational Algebra written by William J. Heinzer and published by American Mathematical Soc.. This book was released on 1994 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Brian MacCrimmon
Publisher :
ISBN 13 :
Total Pages : 144 pages
Book Rating : 4.3/5 (91 download)
Download or read book Strong F-regularity and Boundedness Questions in Tight Closure written by Brian MacCrimmon and published by . This book was released on 1996 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 660 pages
Book Rating : 4.F/5 ( download)
Download or read book Dissertation Abstracts International written by and published by . This book was released on 1993 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Anurag K. Singh
Publisher :
ISBN 13 :
Total Pages : 172 pages
Book Rating : 4.3/5 (91 download)
Download or read book F-regularity, F-rationality and F-purity written by Anurag K. Singh and published by . This book was released on 1998 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Winfried Bruns
Publisher : Cambridge University Press
ISBN 13 : 0521566746
Total Pages : 471 pages
Book Rating : 4.5/5 (215 download)
Download or read book Cohen-Macaulay Rings written by Winfried Bruns and published by Cambridge University Press. This book was released on 1998-06-18 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last two decades Cohen-Macaulay rings and modules have been central topics in commutative algebra. This book meets the need for a thorough, self-contained introduction to the homological and combinatorial aspects of the theory of Cohen-Macaulay rings, Gorenstein rings, local cohomology, and canonical modules. A separate chapter is devoted to Hilbert functions (including Macaulay's theorem) and numerical invariants derived from them. The authors emphasize the study of explicit, specific rings, making the presentation as concrete as possible. So the general theory is applied to Stanley-Reisner rings, semigroup rings, determinantal rings, and rings of invariants. Their connections with combinatorics are highlighted, e.g. Stanley's upper bound theorem or Ehrhart's reciprocity law for rational polytopes. The final chapters are devoted to Hochster's theorem on big Cohen-Macaulay modules and its applications, including Peskine-Szpiro's intersection theorem, the Evans-Griffith syzygy theorem, bounds for Bass numbers, and tight closure. Throughout each chapter the authors have supplied many examples and exercises which, combined with the expository style, will make the book very useful for graduate courses in algebra. As the only modern, broad account of the subject it will be essential reading for researchers in commutative algebra.
Author : Dagmar M. Meyer
Publisher : Cambridge University Press
ISBN 13 : 9780521850643
Total Pages : 210 pages
Book Rating : 4.8/5 (56 download)
Download or read book Poincaré Duality Algebras, Macaulay's Dual Systems, and Steenrod Operations written by Dagmar M. Meyer and published by Cambridge University Press. This book was released on 2005-08-18 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: A monograph demonstrating remarkable and unexpected interdisciplinary connections in the areas of commutative algebra, invariant theory and algebraic topology.
Author : American Mathematical Society
Publisher :
ISBN 13 :
Total Pages : 822 pages
Book Rating : 4.:/5 (43 download)
Download or read book Transactions of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1994-11 with total page 822 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 888 pages
Book Rating : 4.3/5 (91 download)
Download or read book Mathematical Reviews written by and published by . This book was released on 2008 with total page 888 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 796 pages
Book Rating : 4.3/5 (91 download)
Download or read book American Doctoral Dissertations written by and published by . This book was released on 1992 with total page 796 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : American Mathematical Society
Publisher :
ISBN 13 :
Total Pages : 998 pages
Book Rating : 4.:/5 (318 download)
Download or read book Notices of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1993 with total page 998 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Winfried Bruns
Publisher : Springer Nature
ISBN 13 : 3031054806
Total Pages : 514 pages
Book Rating : 4.0/5 (31 download)
Download or read book Determinants, Gröbner Bases and Cohomology written by Winfried Bruns and published by Springer Nature. This book was released on 2022-12-02 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an up-to-date, comprehensive account of determinantal rings and varieties, presenting a multitude of methods used in their study, with tools from combinatorics, algebra, representation theory and geometry. After a concise introduction to Gröbner and Sagbi bases, determinantal ideals are studied via the standard monomial theory and the straightening law. This opens the door for representation theoretic methods, such as the Robinson–Schensted–Knuth correspondence, which provide a description of the Gröbner bases of determinantal ideals, yielding homological and enumerative theorems on determinantal rings. Sagbi bases then lead to the introduction of toric methods. In positive characteristic, the Frobenius functor is used to study properties of singularities, such as F-regularity and F-rationality. Castelnuovo–Mumford regularity, an important complexity measure in commutative algebra and algebraic geometry, is introduced in the general setting of a Noetherian base ring and then applied to powers and products of ideals. The remainder of the book focuses on algebraic geometry, where general vanishing results for the cohomology of line bundles on flag varieties are presented and used to obtain asymptotic values of the regularity of symbolic powers of determinantal ideals. In characteristic zero, the Borel–Weil–Bott theorem provides sharper results for GL-invariant ideals. The book concludes with a computation of cohomology with support in determinantal ideals and a survey of their free resolutions. Determinants, Gröbner Bases and Cohomology provides a unique reference for the theory of determinantal ideals and varieties, as well as an introduction to the beautiful mathematics developed in their study. Accessible to graduate students with basic grounding in commutative algebra and algebraic geometry, it can be used alongside general texts to illustrate the theory with a particularly interesting and important class of varieties.
Author : Winfried Bruns
Publisher : Springer
ISBN 13 : 3540392742
Total Pages : 246 pages
Book Rating : 4.5/5 (43 download)
Download or read book Determinantal Rings written by Winfried Bruns and published by Springer. This book was released on 2006-11-14 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Determinantal rings and varieties have been a central topic of commutative algebra and algebraic geometry. Their study has attracted many prominent researchers and has motivated the creation of theories which may now be considered part of general commutative ring theory. The book gives a first coherent treatment of the structure of determinantal rings. The main approach is via the theory of algebras with straightening law. This approach suggest (and is simplified by) the simultaneous treatment of the Schubert subvarieties of Grassmannian. Other methods have not been neglected, however. Principal radical systems are discussed in detail, and one section is devoted to each of invariant and representation theory. While the book is primarily a research monograph, it serves also as a reference source and the reader requires only the basics of commutative algebra together with some supplementary material found in the appendix. The text may be useful for seminars following a course in commutative ring theory since a vast number of notions, results, and techniques can be illustrated significantly by applying them to determinantal rings.
Author : Ezra Miller
Publisher : Springer Science & Business Media
ISBN 13 : 9780387237077
Total Pages : 442 pages
Book Rating : 4.2/5 (37 download)
Download or read book Combinatorial Commutative Algebra written by Ezra Miller and published by Springer Science & Business Media. This book was released on 2005-06-21 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs
Author : James F. Davis
Publisher : American Mathematical Society
ISBN 13 : 1470473682
Total Pages : 385 pages
Book Rating : 4.4/5 (74 download)
Download or read book Lecture Notes in Algebraic Topology written by James F. Davis and published by American Mathematical Society. This book was released on 2023-05-22 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems. To help students make this transition, the material in this book is presented in an increasingly sophisticated manner. It is intended to bridge the gap between algebraic and geometric topology, both by providing the algebraic tools that a geometric topologist needs and by concentrating on those areas of algebraic topology that are geometrically motivated. Prerequisites for using this book include basic set-theoretic topology, the definition of CW-complexes, some knowledge of the fundamental group/covering space theory, and the construction of singular homology. Most of this material is briefly reviewed at the beginning of the book. The topics discussed by the authors include typical material for first- and second-year graduate courses. The core of the exposition consists of chapters on homotopy groups and on spectral sequences. There is also material that would interest students of geometric topology (homology with local coefficients and obstruction theory) and algebraic topology (spectra and generalized homology), as well as preparation for more advanced topics such as algebraic $K$-theory and the s-cobordism theorem. A unique feature of the book is the inclusion, at the end of each chapter, of several projects that require students to present proofs of substantial theorems and to write notes accompanying their explanations. Working on these projects allows students to grapple with the “big picture”, teaches them how to give mathematical lectures, and prepares them for participating in research seminars. The book is designed as a textbook for graduate students studying algebraic and geometric topology and homotopy theory. It will also be useful for students from other fields such as differential geometry, algebraic geometry, and homological algebra. The exposition in the text is clear; special cases are presented over complex general statements.
