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Author : Eben Matlis
Publisher : Springer
ISBN 13 : 3540469230
Total Pages : 168 pages
Book Rating : 4.5/5 (44 download)
Download or read book One-Dimensional Cohen-Macaulay Rings written by Eben Matlis and published by Springer. This book was released on 2006-11-15 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Eben Matlis
Publisher : Lecture Notes in Mathematics
ISBN 13 :
Total Pages : 178 pages
Book Rating : 4.3/5 (91 download)
Download or read book One-Dimensional Cohen-Macaulay Rings written by Eben Matlis and published by Lecture Notes in Mathematics. This book was released on 1973-06-04 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Eben Matlis
Publisher : Springer
ISBN 13 : 9780387063270
Total Pages : 157 pages
Book Rating : 4.0/5 (632 download)
Download or read book 1-dimensional Cohen-Macaulay Rings written by Eben Matlis and published by Springer. This book was released on 1973-01-01 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 : Graham J. Leuschke
Publisher : American Mathematical Soc.
ISBN 13 : 0821875817
Total Pages : 390 pages
Book Rating : 4.8/5 (218 download)
Download or read book Cohen-Macaulay Representations written by Graham J. Leuschke and published by American Mathematical Soc.. This book was released on 2012-05-02 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive treatment of the representation theory of maximal Cohen-Macaulay (MCM) modules over local rings. This topic is at the intersection of commutative algebra, singularity theory, and representations of groups and algebras. Two introductory chapters treat the Krull-Remak-Schmidt Theorem on uniqueness of direct-sum decompositions and its failure for modules over local rings. Chapters 3-10 study the central problem of classifying the rings with only finitely many indecomposable MCM modules up to isomorphism, i.e., rings of finite CM type. The fundamental material--ADE/simple singularities, the double branched cover, Auslander-Reiten theory, and the Brauer-Thrall conjectures--is covered clearly and completely. Much of the content has never before appeared in book form. Examples include the representation theory of Artinian pairs and Burban-Drozd's related construction in dimension two, an introduction to the McKay correspondence from the point of view of maximal Cohen-Macaulay modules, Auslander-Buchweitz's MCM approximation theory, and a careful treatment of nonzero characteristic. The remaining seven chapters present results on bounded and countable CM type and on the representation theory of totally reflexive modules.
Author : Craig Huneke
Publisher : Cambridge University Press
ISBN 13 : 0521688604
Total Pages : 446 pages
Book Rating : 4.5/5 (216 download)
Download or read book Integral Closure of Ideals, Rings, and Modules written by Craig Huneke and published by Cambridge University Press. This book was released on 2006-10-12 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.
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 : K. Kiyek
Publisher : Springer Science & Business Media
ISBN 13 : 1402020295
Total Pages : 506 pages
Book Rating : 4.4/5 (2 download)
Download or read book Resolution of Curve and Surface Singularities in Characteristic Zero written by K. Kiyek and published by Springer Science & Business Media. This book was released on 2012-09-11 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Curves The Point of View of Max Noether Probably the oldest references to the problem of resolution of singularities are found in Max Noether's works on plane curves [cf. [148], [149]]. And probably the origin of the problem was to have a formula to compute the genus of a plane curve. The genus is the most useful birational invariant of a curve in classical projective geometry. It was long known that, for a plane curve of degree n having l m ordinary singular points with respective multiplicities ri, i E {1, . . . , m}, the genus p of the curve is given by the formula = (n - l)(n - 2) _ ~ "r. (r. _ 1) P 2 2 L. . ,. •• . Of course, the problem now arises: how to compute the genus of a plane curve having some non-ordinary singularities. This leads to the natural question: can we birationally transform any (singular) plane curve into another one having only ordinary singularities? The answer is positive. Let us give a flavor (without proofs) 2 on how Noether did it • To solve the problem, it is enough to consider a special kind of Cremona trans formations, namely quadratic transformations of the projective plane. Let ~ be a linear system of conics with three non-collinear base points r = {Ao, AI, A }, 2 and take a projective frame of the type {Ao, AI, A ; U}.
Author : Idun Reiten
Publisher : American Mathematical Soc.
ISBN 13 : 9780821808504
Total Pages : 216 pages
Book Rating : 4.8/5 (85 download)
Download or read book Algebras and Modules I written by Idun Reiten and published by American Mathematical Soc.. This book was released on 1998 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Surveys developments in the representation theory of finite dimensional algebras and related topics in seven papers illustrating different techniques developed over the recent years. For graduate students and researchers with a background in commutative algebra, including rings, modules, and homological algebra. Suitable as a text for an advanced graduate course. No index. Member prices are $31 for institutions and $23 for individuals, and are available to members of the Canadian Mathematical Society. Annotation copyrighted by Book News, Inc., Portland, OR
Author : Susan M. Cooper
Publisher : Springer
ISBN 13 : 1493906267
Total Pages : 328 pages
Book Rating : 4.4/5 (939 download)
Download or read book Connections Between Algebra, Combinatorics, and Geometry written by Susan M. Cooper and published by Springer. This book was released on 2014-05-16 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra and Geometry contains lecture notes, along with exercises and solutions, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It also contains research and survey papers from academics invited to participate in the companion Special Session on Interactions Between Algebraic Geometry and Commutative Algebra, which was part of the CMS Summer Meeting at the University of Regina held June 2–3, 2012, and the meeting Further Connections Between Algebra and Geometry, which was held at the North Dakota State University February 23, 2013. This volume highlights three mini-courses in the areas of commutative algebra and algebraic geometry: differential graded commutative algebra, secant varieties, and fat points and symbolic powers. It will serve as a useful resource for graduate students and researchers who wish to expand their knowledge of commutative algebra, algebraic geometry, combinatorics, and the intricacies of their intersection.
Author : Irena Peeva
Publisher : CRC Press
ISBN 13 : 1420050915
Total Pages : 305 pages
Book Rating : 4.4/5 (2 download)
Download or read book Syzygies and Hilbert Functions written by Irena Peeva and published by CRC Press. This book was released on 2007-03-20 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilbert functions and resolutions are both central objects in commutative algebra and fruitful tools in the fields of algebraic geometry, combinatorics, commutative algebra, and computational algebra. Spurred by recent research in this area, Syzygies and Hilbert Functions explores fresh developments in the field as well as fundamental concepts.
Author : Daniel Anderson
Publisher : CRC Press
ISBN 13 : 0429530447
Total Pages : 378 pages
Book Rating : 4.4/5 (295 download)
Download or read book Ideal Theoretic Methods in Commutative Algebra written by Daniel Anderson and published by CRC Press. This book was released on 2019-05-07 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes current work of 38 renowned contributors that details the diversity of thought in the fields of commutative algebra and multiplicative ideal theory. Summarizes recent findings on classes of going-down domains and the going-down property, emphasizing new characterizations and applications, as well as generalizations for commutative rings wi
Author : Freddy Van Oystaeyen
Publisher : CRC Press
ISBN 13 : 9780824719906
Total Pages : 340 pages
Book Rating : 4.7/5 (199 download)
Download or read book Commutative Algebra and Algebraic Geometry written by Freddy Van Oystaeyen and published by CRC Press. This book was released on 1999-03-31 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains contributions by over 25 leading international mathematicians in the areas of commutative algebra and algebraic geometry. The text presents developments and results based on, and inspired by, the work of Mario Fiorentini. It covers topics ranging from almost numerical invariants of algebraic curves to deformation of projective schemes.
Author : David Eisenbud
Publisher : Springer Science & Business Media
ISBN 13 : 0387264566
Total Pages : 254 pages
Book Rating : 4.3/5 (872 download)
Download or read book The Geometry of Syzygies written by David Eisenbud and published by Springer Science & Business Media. This book was released on 2006-10-28 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: First textbook-level account of basic examples and techniques in this area. Suitable for self-study by a reader who knows a little commutative algebra and algebraic geometry already. David Eisenbud is a well-known mathematician and current president of the American Mathematical Society, as well as a successful Springer author.
Author : Marco Fontana
Publisher : Walter de Gruyter
ISBN 13 : 3110213184
Total Pages : 395 pages
Book Rating : 4.1/5 (12 download)
Download or read book Commutative Algebra and its Applications written by Marco Fontana and published by Walter de Gruyter. This book was released on 2009-09-04 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains selected refereed papers based on lectures presented at the ‘Fifth International Fez Conference on Commutative Algebra and Applications’ that was held in Fez, Morocco in June 2008. The volume represents new trends and areas of classical research within the field, with contributions from many different countries. In addition, the volume has as a special focus the research and influence of Alain Bouvier on commutative algebra over the past thirty years.
Author : Maria Evelina Rossi
Publisher : Springer Science & Business Media
ISBN 13 : 3642142400
Total Pages : 115 pages
Book Rating : 4.6/5 (421 download)
Download or read book Hilbert Functions of Filtered Modules written by Maria Evelina Rossi and published by Springer Science & Business Media. This book was released on 2010-08-25 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilbert Functions play major roles in Algebraic Geometry and Commutative Algebra, and are becoming increasingly important also in Computational Algebra. They capture many useful numerical characters associated to a projective variety or to a filtered module over a local ring. Starting from the pioneering work of D.G. Northcott and J. Sally, we aim to gather together in one place many new developments of this theory by using a unifying approach which gives self-contained and easier proofs. The extension of the theory to the case of general filtrations on a module, and its application to the study of certain graded algebras which are not associated to a filtration are two of the main features of the monograph. The material is intended for graduate students and researchers who are interested in Commutative Algebra, in particular in the theory of the Hilbert Functions and related topics.
Author : Gert-Martin Greuel
Publisher : Springer Science & Business Media
ISBN 13 : 9783540428978
Total Pages : 640 pages
Book Rating : 4.4/5 (289 download)
Download or read book A Singular Introduction to Commutative Algebra written by Gert-Martin Greuel and published by Springer Science & Business Media. This book was released on 2002 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: CD-ROM contains: "a version of Singular for various platforms (Unix/Linux, Windows, Macintosh:, including all examples and procedures explained in the book."
