Download or read book One dimensional Local Rings of Infinite Cohen Macaulay Type written by Silvia Saccon and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

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:

Download or read book Representation Theory of One dimensional Local Rings of Finite Cohen Macaulay Type written by Nicholas R. Baeth and published by . This book was released on 2005 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

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:

Download or read book Maximal Cohen Macaulay Modules and Tate Cohomology written by Ragnar-Olaf Buchweitz and published by American Mathematical Society. This book was released on 2021-12-16 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a lightly edited version of the unpublished manuscript Maximal Cohen–Macaulay modules and Tate cohomology over Gorenstein rings by Ragnar-Olaf Buchweitz. The central objects of study are maximal Cohen–Macaulay modules over (not necessarily commutative) Gorenstein rings. The main result is that the stable category of maximal Cohen–Macaulay modules over a Gorenstein ring is equivalent to the stable derived category and also to the homotopy category of acyclic complexes of projective modules. This assimilates and significantly extends earlier work of Eisenbud on hypersurface singularities. There is also an extensive discussion of duality phenomena in stable derived categories, extending Tate duality on cohomology of finite groups. Another noteworthy aspect is an extension of the classical BGG correspondence to super-algebras. There are numerous examples that illustrate these ideas. The text includes a survey of developments subsequent to, and connected with, Buchweitz's manuscript.

Download or read book Commutative Algebra written by Marco Fontana and published by Springer Science & Business Media. This book was released on 2010-09-29 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: Commutative algebra is a rapidly growing subject that is developing in many different directions. This volume presents several of the most recent results from various areas related to both Noetherian and non-Noetherian commutative algebra. This volume contains a collection of invited survey articles by some of the leading experts in the field. The authors of these chapters have been carefully selected for their important contributions to an area of commutative-algebraic research. Some topics presented in the volume include: generalizations of cyclic modules, zero divisor graphs, class semigroups, forcing algebras, syzygy bundles, tight closure, Gorenstein dimensions, tensor products of algebras over fields, as well as many others. This book is intended for researchers and graduate students interested in studying the many topics related to commutative algebra.

Download or read book Rings Modules and Representations written by Viet Dung Nguyen and published by American Mathematical Soc.. This book was released on 2009 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume contain results in active research areas in the theory of rings and modules, including non commutative and commutative ring theory, module theory, representation theory, and coding theory.

Download or read book Lecture Notes on Local Rings written by Birger Iversen and published by World Scientific Publishing Company Incorporated. This book was released on 2014 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Dimension of a local ring. 1.1. Nakayama's lemma. 1.2. Prime ideals. 1.3. Noetherian modules. 1.4. Modules of finite length. 1.5. Hilbert's basis theorem. 1.6. Graded rings. 1.7. Filtered rings. 1.8. Local rings. 1.9. Regular local rings -- 2. Modules over a local ring. 2.1. Support of a module. 2.2. Associated prime ideals. 2.3. Dimension of a module. 2.4. Depth of a module. 2.5. Cohen-Macaulay modules. 2.6. Modules of finite projective dimension. 2.7. The Koszul complex. 2.8. Regular local rings. 2.9. Projective dimension and depth -- 2.10. [symbol]-depth. 2.11. The acyclicity theorem. 2.12. An example -- 3. Divisor theory. 3.1. Discrete valuation rings. 3.2. Normal domains. 3.3. Divisors. 3.4. Unique factorization. 3.5. Torsion modules. 3.6. The first Chern class. 3.7. Regular local rings. 3.8. Picard groups. 3.9. Dedekind domains -- 4. Completion. 4.1. Exactness of the completion functor. 4.2. Separation of the [symbol]-adic topology. 4.3. Complete filtered rings. 4.4. Completion of local rings. 4.5. Structure of complete local rings -- 5. Injective modules. 5.1. Injective modules. 5.2. Injective envelopes. 5.3. Decomposition of injective modules. 5.4. Matlis duality. 5.5. Minimal injective resolutions. 5.6. Modules of finite injective dimension. 5.7. Gorenstein rings -- 6. Local cohomology. 6.1. Basic properties. 6.2. Local cohomology and dimension. 6.3. Local cohomology and depth. 6.4. Support in the maximal ideal. 6.5. Local duality for Gorenstein rings -- 7. Dualizing complexes. 7.1. Complexes of injective modules. 7.2. Complexes with finitely generated cohomology. 7.3. The evaluation map. 7.4. Existence of dualizing complexes. 7.5. The codimension function. 7.6. Complexes of flat modules. 7.7. Generalized evaluation maps. 7.8. Uniqueness of dualizing complexes -- 8. Local duality. 8.1. Poincare series. 8.2. Grothendieck's local duality theorem. 8.3. Duality for Cohen-Macaulay modules. 8.4. Dualizing modules. 8.5. Locally factorial domains. 8.6. Conductors. 8.7. Formal fibers -- 9. Amplitude and dimension. 9.1. Depth of a complex. 9.2. The dual of a module. 9.3. The amplitude formula. 9.4. Dimension of a complex. 9.5. The tensor product formula. 9.6. Depth inequalities. 9.7. Condition Sr of Serre. 9.8. Factorial rings and condition Sr. 9.9. Condition S[symbol]. 9.10. Specialization of Poincare series -- 10. Intersection multiplicities. 10.1. Introduction to Serre's conjectures. 10.2. Filtration of the Koszul complex. 10.3. Euler characteristic of the Koszul complex. 10.4. A projection formula. 10.5. Power series over a field. 10.6. Power series over a discrete valuation ring. 10.7. Application of Cohen's structure theorem. 10.8. The amplitude inequality. 10.9. Translation invariant operators. 10.10. Todd operators. 10.11. Serre's conjecture in the graded case -- 11. Complexes of free modules. 11.1. McCoy's theorem. 11.2. The rank of a linear map. 11.3. The Eisenbud-Buchsbaum criterion. 11.4. Fitting's ideals. 11.5. The Euler characteristic. 11.6. McRae's invariant. 11.7. The integral character of McRae's invariant

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.

Download or read book On Cohen Macaulay Local Rings of Dimension One and Embedding Dimension Two written by H. A. Tavallaee and published by . This book was released on 1982 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Download or read book Abelian Groups Rings Modules and Homological Algebra written by Pat Goeters and published by CRC Press. This book was released on 2016-04-19 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: About the book In honor of Edgar Enochs and his venerable contributions to a broad range of topics in Algebra, top researchers from around the world gathered at Auburn University to report on their latest work and exchange ideas on some of today's foremost research topics. This carefully edited volume presents the refereed papers of the par

Download or read book Commutative Algebra written by Irena Peeva and published by Springer Science & Business Media. This book was released on 2013-02-01 with total page 705 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume brings together the highest quality expository papers written by leaders and talented junior mathematicians in the field of Commutative Algebra. Contributions cover a very wide range of topics, including core areas in Commutative Algebra and also relations to Algebraic Geometry, Algebraic Combinatorics, Hyperplane Arrangements, Homological Algebra, and String Theory. The book aims to showcase the area, especially for the benefit of junior mathematicians and researchers who are new to the field; it will aid them in broadening their background and to gain a deeper understanding of the current research in this area. Exciting developments are surveyed and many open problems are discussed with the aspiration to inspire the readers and foster further research.

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.

Download or read book Integral Domains Inside Noetherian Power Series Rings Constructions and Examples written by William Heinzer and published by American Mathematical Soc.. This book was released on 2021-10-08 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Power series provide a technique for constructing examples of commutative rings. In this book, the authors describe this technique and use it to analyse properties of commutative rings and their spectra. This book presents results obtained using this approach. The authors put these results in perspective; often the proofs of properties of classical examples are simplified. The book will serve as a helpful resource for researchers working in commutative algebra.

Download or read book Algebraic Geometry and its Applications written by Chandrajit L. Bajaj and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic Geometry and its Applications will be of interest not only to mathematicians but also to computer scientists working on visualization and related topics. The book is based on 32 invited papers presented at a conference in honor of Shreeram Abhyankar's 60th birthday, which was held in June 1990 at Purdue University and attended by many renowned mathematicians (field medalists), computer scientists and engineers. The keynote paper is by G. Birkhoff; other contributors include such leading names in algebraic geometry as R. Hartshorne, J. Heintz, J.I. Igusa, D. Lazard, D. Mumford, and J.-P. Serre.