Author: Lars W. Christensen
Publisher: Springer
ISBN: 3540400087
Category : Mathematics
Languages : en
Pages : 209
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Book Description
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.
Author: Marco A. P. Bullones
Publisher: CRC Press
ISBN: 149872535X
Category : Mathematics
Languages : en
Pages : 370
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Book Description
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.
Author: Alina Iacob
Publisher: CRC Press
ISBN: 1351660268
Category : Mathematics
Languages : en
Pages : 214
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Book Description
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.
Author: Marco A. P. Bullones
Publisher: CRC Press
ISBN: 1315353466
Category : Mathematics
Languages : en
Pages : 347
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Book Description
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.
Author: Maurice Auslander
Publisher: American Mathematical Soc.
ISBN: 0821812947
Category : Commutative rings
Languages : en
Pages : 150
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Book Description
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.
Author: Lars Winther Christensen
Publisher:
ISBN:
Category :
Languages : en
Pages : 22
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Book Description
Author: Nathan Gorenstein
Publisher: Simon and Schuster
ISBN: 1982129220
Category : Biography & Autobiography
Languages : en
Pages : 344
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Book Description
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.
Author:
Publisher:
ISBN:
Category :
Languages : da
Pages : 22
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Book Description
Author: Edgar E. Enochs
Publisher: Nova Biomedical Books
ISBN: 9781590330180
Category : Gorenstein rings
Languages : en
Pages : 0
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Book Description
Gorenstein Flat Modules
Author: Mariagrazia Bianchi
Publisher: World Scientific
ISBN: 9814350389
Category : Mathematics
Languages : en
Pages : 416
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Book Description
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.
