Gorenstein Dimensions
Gorenstein Dimensions

Author: Lars W. Christensen

Publisher: Springer

Published: 2007-05-06

Total Pages: 209

ISBN-13: 3540400087

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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.

Gorenstein Homological Algebra
Gorenstein Homological Algebra

Author: Alina Iacob

Publisher: CRC Press

Published: 2018-08-06

Total Pages: 214

ISBN-13: 1351660268

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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.

Introduction to Abelian Model Structures and Gorenstein Homological Dimensions
Introduction to Abelian Model Structures and Gorenstein Homological Dimensions

Author: Marco A. P. Bullones

Publisher: CRC Press

Published: 2016-08-19

Total Pages: 347

ISBN-13: 1315353466

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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.

Stable Module Theory
Stable Module Theory

Author: Maurice Auslander

Publisher: American Mathematical Soc.

Published: 1969

Total Pages: 150

ISBN-13: 0821812947

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The notions of torsion and torsion freeness have played a very important role in module theory--particularly in the study of modules over integral domains. Furthermore, the use of homological techniques in this connection has been well established. It is the aim of this paper to extend these techniques and to show that this extension leads naturally to several new concepts (e.g. k-torsion freeness and Gorenstein dimension) which are useful in the classification of modules and rings.

Ischia Group Theory 2010
Ischia Group Theory 2010

Author: Mariagrazia Bianchi

Publisher: World Scientific

Published: 2012

Total Pages: 416

ISBN-13: 9814350389

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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.

Progress in Commutative Algebra 1
Progress in Commutative Algebra 1

Author: Christopher Francisco

Publisher: Walter de Gruyter

Published: 2012-04-26

Total Pages: 377

ISBN-13: 3110250403

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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.

Abelian Groups, Rings, Modules, and Homological Algebra
Abelian Groups, Rings, Modules, and Homological Algebra

Author: Pat Goeters

Publisher: CRC Press

Published: 2016-04-19

Total Pages: 354

ISBN-13: 142001076X

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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

Commutative Algebra
Commutative Algebra

Author: Marco Fontana

Publisher: Springer Science & Business Media

Published: 2010-09-29

Total Pages: 491

ISBN-13: 144196990X

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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.

The Guns of John Moses Browning
The Guns of John Moses Browning

Author: Nathan Gorenstein

Publisher: Simon and Schuster

Published: 2021-05-25

Total Pages: 336

ISBN-13: 1982129239

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A “well-researched and very readable new biography” (The Wall Street Journal) of “the Thomas Edison of guns,” a visionary inventor who designed the modern handgun and whose awe-inspiring array of firearms helped ensure victory in numerous American wars and holds a crucial place in world history. Few people are aware that John Moses Browning—a tall, humble, cerebral man born in 1855 and raised as a Mormon in the American West—was the mind behind many of the world-changing firearms that dominated more than a century of conflict. He invented the design used in virtually all modern pistols, created the most popular hunting rifles and shotguns, and conceived the machine guns that proved decisive not just in World Wars I and II but nearly every major military action since. Yet few in America knew his name until he was into his sixties. Now, author Nathan Gorenstein brings firearms inventor John Moses Browning to vivid life in this riveting and revealing biography. Embodying the tradition of self-made, self-educated geniuses (like Lincoln and Edison), Browning was able to think in three dimensions (he never used blueprints) and his gifted mind produced everything from the famous Winchester “30-30” hunting rifle to the awesomely effective machine guns used by every American aircraft and infantry unit in World War II. The British credited Browning’s guns with helping to win the Battle of Britain. His inventions illustrate both the good and bad of weapons. Sweeping, lively, and brilliantly told, this fascinating book that “gun collectors and historians of armaments will cherish” (Kirkus Reviews) introduces a little-known legend whose impact on history ranks with that of the Wright Brothers, Thomas Edison, and Henry Ford.