Gorenstein Dimensions

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Gorenstein Dimensions

Lars W. Christensen
Gorenstein Dimensions Book PDF

Author : Lars W. Christensen
Publisher : Springer
Page : 209 pages
File Size : 45,6 Mb
Release : 2007-05-06
Category : Mathematics
ISBN : 9783540400080

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Gorenstein Dimensions by Lars W. Christensen Pdf

This book is intended as a reference for mathematicians working with homological dimensions in commutative algebra and as an introduction to Gorenstein dimensions for graduate students with an interest in the same. Any admirer of classics like the Auslander-Buchsbaum-Serre characterization of regular rings, and the Bass and Auslander-Buchsbaum formulas for injective and projective dimension of f.g. modules will be intrigued by this book's content. Readers should be well-versed in commutative algebra and standard applications of homological methods. The framework is that of complexes, but all major results are restated for modules in traditional notation, and an appendix makes the proofs accessible for even the casual user of hyperhomological methods.

Introduction to Abelian Model Structures and Gorenstein Homological Dimensions

Marco A. P. Bullones
Introduction to Abelian Model Structures and Gorenstein Homological Dimensions Book PDF

Author : Marco A. P. Bullones
Publisher : CRC Press
Page : 309 pages
File Size : 55,8 Mb
Release : 2016-08-19
Category : Mathematics
ISBN : 9781315353463

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Introduction to Abelian Model Structures and Gorenstein Homological Dimensions by Marco A. P. Bullones Pdf

Introduction to Abelian Model Structures and Gorenstein Homological Dimensions provides a starting point to study the relationship between homological and homotopical algebra, a very active branch of mathematics. The book shows how to obtain new model structures in homological algebra by constructing a pair of compatible complete cotorsion pairs related to a specific homological dimension and then applying the Hovey Correspondence to generate an abelian model structure. The first part of the book introduces the definitions and notations of the universal constructions most often used in category theory. The next part presents a proof of the Eklof and Trlifaj theorem in Grothedieck categories and covers M. Hovey’s work that connects the theories of cotorsion pairs and model categories. The final two parts study the relationship between model structures and classical and Gorenstein homological dimensions and explore special types of Grothendieck categories known as Gorenstein categories. As self-contained as possible, this book presents new results in relative homological algebra and model category theory. The author also re-proves some established results using different arguments or from a pedagogical point of view. In addition, he proves folklore results that are difficult to locate in the literature.

Commutative Algebra and Its Applications

Marco Fontana
Commutative Algebra and Its Applications Book PDF

Author : Marco Fontana
Publisher : Walter de Gruyter
Page : 395 pages
File Size : 49,7 Mb
Release : 2009
Category : Mathematics
ISBN : 9783110207460

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Commutative Algebra and Its Applications by Marco Fontana Pdf

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.

Commutative Algebra

Marco Fontana,Salah-Eddine Kabbaj,Bruce Olberding,Irena Swanson
Commutative Algebra Book PDF

Author : Marco Fontana,Salah-Eddine Kabbaj,Bruce Olberding,Irena Swanson
Publisher : Springer Science & Business Media
Page : 491 pages
File Size : 49,5 Mb
Release : 2010-09-29
Category : Mathematics
ISBN : 9781441969903

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Commutative Algebra by Marco Fontana,Salah-Eddine Kabbaj,Bruce Olberding,Irena Swanson Pdf

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.

Progress in Commutative Algebra 1

Christopher Francisco,Lee C. Klingler,Sean Sather-Wagstaff,Janet C. Vassilev
Progress in Commutative Algebra 1 Book PDF

Author : Christopher Francisco,Lee C. Klingler,Sean Sather-Wagstaff,Janet C. Vassilev
Publisher : Walter de Gruyter
Page : 377 pages
File Size : 49,6 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9783110250404

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Progress in Commutative Algebra 1 by Christopher Francisco,Lee C. Klingler,Sean Sather-Wagstaff,Janet C. Vassilev Pdf

This is the first of two volumes of a state-of-the-art survey article collection which originates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. These volumes present current trends in two of the most active areas of commutative algebra: non-noetherian rings (factorization, ideal theory, integrality), and noetherian rings (the local theory, graded situation, and interactions with combinatorics and geometry). This volume contains combinatorial and homological surveys. The combinatorial papers document some of the increasing focus in commutative algebra recently on the interaction between algebra and combinatorics. Specifically, one can use combinatorial techniques to investigate resolutions and other algebraic structures as with the papers of Fløystad on Boij-Söderburg theory, of Geramita, Harbourne and Migliore, and of Cooper on Hilbert functions, of Clark on minimal poset resolutions and of Mermin on simplicial resolutions. One can also utilize algebraic invariants to understand combinatorial structures like graphs, hypergraphs, and simplicial complexes such as in the paper of Morey and Villarreal on edge ideals. Homological techniques have become indispensable tools for the study of noetherian rings. These ideas have yielded amazing levels of interaction with other fields like algebraic topology (via differential graded techniques as well as the foundations of homological algebra), analysis (via the study of D-modules), and combinatorics (as described in the previous paragraph). The homological articles the editors have included in this volume relate mostly to how homological techniques help us better understand rings and singularities both noetherian and non-noetherian such as in the papers by Roberts, Yao, Hummel and Leuschke.

Algebra and Its Applications

Dinh Van Huynh,Surender Kumar Jain,Sergio R. López-Permouth
Algebra and Its Applications Book PDF

Author : Dinh Van Huynh,Surender Kumar Jain,Sergio R. López-Permouth
Publisher : American Mathematical Soc.
Page : 586 pages
File Size : 47,5 Mb
Release : 2000
Category : Mathematics
ISBN : 9780821819500

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Algebra and Its Applications by Dinh Van Huynh,Surender Kumar Jain,Sergio R. López-Permouth Pdf

Among all areas of mathematics, algebra is one of the best suited to find applications within the frame of our booming technological society. The thirty-eight articles in this volume encompass the proceedings of the International Conference on Algebra and Its Applications (Athens, OH, 1999), which explored the applications and interplay among the disciplines of ring theory, linear algebra, and coding theory. The presentations collected here reflect the dialogue between mathematicians involved in theoretical aspects of algebra and mathematicians involved in solving problems where state-of-the-art research tools may be used and applied. This Contemporary Mathematics series volume communicates the potential for collaboration among those interested in exploring the wealth of applications for abstract algebra in fields such as information and coding. The expository papers would serve well as supplemental reading in graduate seminars.

Algebra and Coding Theory

A. Leroy,S. K. Jain
Algebra and Coding Theory Book PDF

Author : A. Leroy,S. K. Jain
Publisher : American Mathematical Society
Page : 270 pages
File Size : 46,9 Mb
Release : 2023-05-01
Category : Mathematics
ISBN : 9781470468590

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Algebra and Coding Theory by A. Leroy,S. K. Jain Pdf

This volume contains the proceedings of the Virtual Conference on Noncommutative Rings and their Applications VII, in honor of Tariq Rizvi, held from July 5–7, 2021, and the Virtual Conference on Quadratic Forms, Rings and Codes, held on July 8, 2021, both of which were hosted by the Université d'Artois, Lens, France. The articles cover topics in commutative and noncommutative algebra and applications to coding theory. In some papers, applications of Frobenius rings, the skew group rings, and iterated Ore extensions to coding theory are discussed. Other papers discuss classical topics, such as Utumi rings, Baer rings, nil and nilpotent algebras, and Brauer groups. Still other articles are devoted to various aspects of the elementwise study for rings and modules. Lastly, this volume includes papers dealing with questions in homological algebra and lattice theory. The articles in this volume show the vivacity of the research of noncommutative rings and its influence on other subjects.

Ischia Group Theory 2010

Mariagrazia Bianchi,Mariagrazia Bianchi Oddera,Patrizia Longobardi,Mercede Maj
Ischia Group Theory 2010 Book PDF

Author : Mariagrazia Bianchi,Mariagrazia Bianchi Oddera,Patrizia Longobardi,Mercede Maj
Publisher : World Scientific
Page : 416 pages
File Size : 52,7 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814350389

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Ischia Group Theory 2010 by Mariagrazia Bianchi,Mariagrazia Bianchi Oddera,Patrizia Longobardi,Mercede Maj Pdf

The papers in this volume represent the proceedings of the Conference entitled "Ischia Group Theory 2010," which took place at NH Ischia Thermal SPA Resort, Ischia, Naples, Italy, from April 14 to April 17, 2010. The articles in this volume are contributions by speakers and participants of the Conference. The volume contains a collection of research articles by leading experts in group theory and some accessible surveys of recent research in the area. Together they provide an overview of the diversity of themes and applications that interest group theorists today. Topics covered in this volume include: finite p-groups, character and representation theory, combinatorial group theory, varieties of groups, profinite and pro-p-groups, linear groups, graphs connected with groups, subgroup structure, finiteness conditions, radical rings, conjugacy classes, automorphisms.

Geometric and Cohomological Group Theory

Peter H. Kropholler,Ian J. Leary,Conchita Martínez-Pérez,Brita E. A. Nucinkis
Geometric and Cohomological Group Theory Book PDF

Author : Peter H. Kropholler,Ian J. Leary,Conchita Martínez-Pérez,Brita E. A. Nucinkis
Publisher : Cambridge University Press
Page : 277 pages
File Size : 50,5 Mb
Release : 2018
Category : Mathematics
ISBN : 9781316623220

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Geometric and Cohomological Group Theory by Peter H. Kropholler,Ian J. Leary,Conchita Martínez-Pérez,Brita E. A. Nucinkis Pdf

Surveys the state of the art in geometric and cohomological group theory. Ideal entry point for young researchers.

Abelian Groups, Rings, Modules, and Homological Algebra

Pat Goeters,Overtoun M.G. Jenda
Abelian Groups Rings Modules and Homological Algebra Book PDF

Author : Pat Goeters,Overtoun M.G. Jenda
Publisher : CRC Press
Page : 354 pages
File Size : 46,6 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9781420010763

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Abelian Groups, Rings, Modules, and Homological Algebra by Pat Goeters,Overtoun M.G. Jenda Pdf

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

Foundations of Commutative Rings and Their Modules

Fanggui Wang,Hwankoo Kim
Foundations of Commutative Rings and Their Modules Book PDF

Author : Fanggui Wang,Hwankoo Kim
Publisher : Springer
Page : 699 pages
File Size : 52,9 Mb
Release : 2017-01-06
Category : Mathematics
ISBN : 9789811033377

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Foundations of Commutative Rings and Their Modules by Fanggui Wang,Hwankoo Kim Pdf

This book provides an introduction to the basics and recent developments of commutative algebra. A glance at the contents of the first five chapters shows that the topics covered are ones that usually are included in any commutative algebra text. However, the contents of this book differ significantly from most commutative algebra texts: namely, its treatment of the Dedekind–Mertens formula, the (small) finitistic dimension of a ring, Gorenstein rings, valuation overrings and the valuative dimension, and Nagata rings. Going further, Chapter 6 presents w-modules over commutative rings as they can be most commonly used by torsion theory and multiplicative ideal theory. Chapter 7 deals with multiplicative ideal theory over integral domains. Chapter 8 collects various results of the pullbacks, especially Milnor squares and D+M constructions, which are probably the most important example-generating machines. In Chapter 9, coherent rings with finite weak global dimensions are probed, and the local ring of weak global dimension two is elaborated on by combining homological tricks and methods of star operation theory. Chapter 10 is devoted to the Grothendieck group of a commutative ring. In particular, the Bass–Quillen problem is discussed. Finally, Chapter 11 aims to introduce relative homological algebra, especially where the related concepts of integral domains which appear in classical ideal theory are defined and investigated by using the class of Gorenstein projective modules. Each section of the book is followed by a selection of exercises of varying degrees of difficulty. This book will appeal to a wide readership from graduate students to academic researchers who are interested in studying commutative algebra.

Introduction to Abelian Model Structures and Gorenstein Homological Dimensions

Marco A. P. Bullones
Introduction to Abelian Model Structures and Gorenstein Homological Dimensions Book PDF

Author : Marco A. P. Bullones
Publisher : CRC Press
Page : 370 pages
File Size : 42,8 Mb
Release : 2016-08-19
Category : Mathematics
ISBN : 9781498725354

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Introduction to Abelian Model Structures and Gorenstein Homological Dimensions by Marco A. P. Bullones Pdf

Introduction to Abelian Model Structures and Gorenstein Homological Dimensions provides a starting point to study the relationship between homological and homotopical algebra, a very active branch of mathematics. The book shows how to obtain new model structures in homological algebra by constructing a pair of compatible complete cotorsion pairs related to a specific homological dimension and then applying the Hovey Correspondence to generate an abelian model structure. The first part of the book introduces the definitions and notations of the universal constructions most often used in category theory. The next part presents a proof of the Eklof and Trlifaj theorem in Grothedieck categories and covers M. Hovey’s work that connects the theories of cotorsion pairs and model categories. The final two parts study the relationship between model structures and classical and Gorenstein homological dimensions and explore special types of Grothendieck categories known as Gorenstein categories. As self-contained as possible, this book presents new results in relative homological algebra and model category theory. The author also re-proves some established results using different arguments or from a pedagogical point of view. In addition, he proves folklore results that are difficult to locate in the literature.

Relative Homological Algebra

Edgar E. Enochs,Overtoun M. G. Jenda
Relative Homological Algebra Book PDF

Author : Edgar E. Enochs,Overtoun M. G. Jenda
Publisher : Walter de Gruyter
Page : 377 pages
File Size : 49,9 Mb
Release : 2011-10-27
Category : Mathematics
ISBN : 9783110215212

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Relative Homological Algebra by Edgar E. Enochs,Overtoun M. G. Jenda Pdf

This is the second revised edition of an introduction to contemporary relative homological algebra. It supplies important material essential to understand topics in algebra, algebraic geometry and algebraic topology. Each section comes with exercises providing practice problems for students as well as additional important results for specialists. In this new edition the authors have added well-known additional material in the first three chapters, and added new material that was not available at the time the original edition was published. In particular, the major changes are the following: Chapter 1: Section 1.2 has been rewritten to clarify basic notions for the beginner, and this has necessitated a new Section 1.3. Chapter 3: The classic work of D. G. Northcott on injective envelopes and inverse polynomials is finally included. This provides additional examples for the reader. Chapter 11: Section 11.9 on Kaplansky classes makes volume one more up to date. The material in this section was not available at the time the first edition was published. The authors also have clarified some text throughout the book and updated the bibliography by adding new references. The book is also suitable for an introductory course in commutative and ordinary homological algebra.

Gorenstein Homological Algebra

Alina Iacob
Gorenstein Homological Algebra Book PDF

Author : Alina Iacob
Publisher : CRC Press
Page : 219 pages
File Size : 40,9 Mb
Release : 2018-08-06
Category : Mathematics
ISBN : 9781351660259

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Gorenstein Homological Algebra by Alina Iacob Pdf

Gorenstein homological algebra is an important area of mathematics, with applications in commutative and noncommutative algebra, model category theory, representation theory, and algebraic geometry. While in classical homological algebra the existence of the projective, injective, and flat resolutions over arbitrary rings are well known, things are a little different when it comes to Gorenstein homological algebra. The main open problems in this area deal with the existence of the Gorenstein injective, Gorenstein projective, and Gorenstein flat resolutions. Gorenstein Homological Algebra is especially suitable for graduate students interested in homological algebra and its applications.

Extended Abstracts Spring 2015

Dolors Herbera,Wolfgang Pitsch,Santiago Zarzuela
Extended Abstracts Spring 2015 Book PDF

Author : Dolors Herbera,Wolfgang Pitsch,Santiago Zarzuela
Publisher : Birkhäuser
Page : 192 pages
File Size : 48,7 Mb
Release : 2016-11-30
Category : Mathematics
ISBN : 9783319454412

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Extended Abstracts Spring 2015 by Dolors Herbera,Wolfgang Pitsch,Santiago Zarzuela Pdf

This book includes 33 expanded abstracts of selected talks given at the two workshops "Homological Bonds Between Commutative Algebra and Representation Theory" and "Brave New Algebra: Opening Perspectives," and the conference "Opening Perspectives in Algebra, Representations, and Topology," held at the Centre de Recerca Matemàtica (CRM) in Barcelona between January and June 2015. These activities were part of the one-semester intensive research program "Interactions Between Representation Theory, Algebraic Topology and Commutative Algebra (IRTATCA)." Most of the abstracts present preliminary versions of not-yet published results and cover a large number of topics (including commutative and non commutative algebra, algebraic topology, singularity theory, triangulated categories, representation theory) overlapping with homological methods. This comprehensive book is a valuable resource for the community of researchers interested in homological algebra in a broad sense, and those curious to learn the latest developments in the area. It appeals to established researchers as well as PhD and postdoctoral students who want to learn more about the latest advances in these highly active fields of research.