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Homological Algebra

Homological Algebra Author Marco Grandis
ISBN-10 9789814425926
Release 2013
Pages 356
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This book proposes a study of semi-exact homological categories as a basis for a generalized homological algebra. The aim is to extend homological notions to deeply non-abelian situations, where satellites and spectral sequences produced by unstable homotopy can still be studied.



Abelian Groups Rings Modules and Homological Algebra

Abelian Groups  Rings  Modules  and Homological Algebra Author Pat Goeters
ISBN-10 1584885521
Release 2006-01-27
Pages 360
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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 participants of these talks along with contributions from other veteran researchers who were unable to attend. These papers reflect many of the current topics in Abelian Groups, Commutative Algebra, Commutative Rings, Group Theory, Homological Algebra, Lie Algebras, and Module Theory. Accessible even to beginning mathematicians, many of these articles suggest problems and programs for future study. This volume is an outstanding addition to the literature and a valuable handbook for beginning as well as seasoned researchers in Algebra. about the editors... H. PAT GOETERS completed his undergraduate studies in mathematics and computer science at Southern Connecticut State University and received his Ph.D. in 1984 from the University of Connecticut under the supervision of William J. Wickless. After spending one year in a post-doctoral position in Wesleyan University under the tutelage of James D. Reid, Goeters was invited for a tenure track position in Auburn University by Ulrich F. Albrecht. Soon afterwards, William Ullery and Overtoun Jenda were hired, and so began a lively Algebra group. OVERTOUN M. G. JENDA received his bachelor's degree in Mathematics from Chancellor College, the University of Malawi. He moved to the U.S. 1977 to pursue graduate studies at University of Kentucky, earning his Ph.D. in 1981 under the supervision of Professor Edgar Enochs. He then returned to Chancellor College, where he was a lecturer (assistant professor) for three years. He moved to the University of Botswana for another three-year stint as a lecturer before moving back to the University of Kentucky as a visiting assistant professor in 1987. In 1988, he joined the Algebra research group at Auburn University.



A Singular Introduction to Commutative Algebra

A Singular Introduction to Commutative Algebra Author Gert-Martin Greuel
ISBN-10 9783540735427
Release 2007-09-23
Pages 689
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This substantially enlarged second edition aims to lead a further stage in the computational revolution in commutative algebra. This is the first handbook/tutorial to extensively deal with SINGULAR. Among the book’s most distinctive features is a new, completely unified treatment of the global and local theories. Another feature of the book is its breadth of coverage of theoretical topics in the portions of commutative algebra closest to algebraic geometry, with algorithmic treatments of almost every topic.



Introduction to Commutative Algebra and Algebraic Geometry

Introduction to Commutative Algebra and Algebraic Geometry Author Ernst Kunz
ISBN-10 0817630651
Release 1985
Pages 238
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Introduction to Commutative Algebra and Algebraic Geometry has been writing in one form or another for most of life. You can find so many inspiration from Introduction to Commutative Algebra and Algebraic Geometry also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Introduction to Commutative Algebra and Algebraic Geometry book for free.



Set theoretic methods in homological algebra and Abelian groups

Set theoretic methods in homological algebra and Abelian groups Author Paul C. Eklof
ISBN-10 UOM:39015017308928
Release 1980
Pages 117
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Set theoretic methods in homological algebra and Abelian groups has been writing in one form or another for most of life. You can find so many inspiration from Set theoretic methods in homological algebra and Abelian groups also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Set theoretic methods in homological algebra and Abelian groups book for free.



Mal cev Protomodular Homological and Semi Abelian Categories

Mal cev  Protomodular  Homological and Semi Abelian Categories Author Francis Borceux
ISBN-10 1402019610
Release 2004-02-29
Pages 479
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The purpose of the book is to take stock of the situation concerning Algebra via Category Theory in the last fifteen years, where the new and synthetic notions of Mal'cev, protomodular, homological and semi-abelian categories emerged. These notions force attention on the fibration of points and allow a unified treatment of the main algebraic: homological lemmas, Noether isomorphisms, commutator theory. The book gives full importance to examples and makes strong connections with Universal Algebra. One of its aims is to allow appreciating how productive the essential categorical constraint is: knowing an object, not from inside via its elements, but from outside via its relations with its environment. The book is intended to be a powerful tool in the hands of researchers in category theory, homology theory and universal algebra, as well as a textbook for graduate courses on these topics.



Operator Algebras Operator Theory and Applications

Operator Algebras  Operator Theory and Applications Author J. J. Grobler
ISBN-10 3034601743
Release 2009-12-24
Pages 294
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Operator Algebras Operator Theory and Applications has been writing in one form or another for most of life. You can find so many inspiration from Operator Algebras Operator Theory and Applications also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Operator Algebras Operator Theory and Applications book for free.



Extended Abstracts Spring 2015

Extended Abstracts Spring 2015 Author Dolors Herbera
ISBN-10 9783319454412
Release 2016-12-14
Pages 192
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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.



A Non Hausdorff Completion

A Non Hausdorff Completion Author Saul Lubkin
ISBN-10 9789814667401
Release 2015-05-28
Pages 352
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This book introduces entirely new invariants never considered before, in homological algebra and commutative (and even non-commutative) algebra. The C-completion C(M), and higher C-completions, Cn(M), are defined for an arbitrary left module M over a topological ring A. Spectral sequences are defined that use these invariants. Given a left module over a topological ring A, under mild conditions the usual Hausdorff completion: M^ can be recovered from the C-completion C(M), by taking the quotient module by the closure of {0}. The new invariants and tools in this book are expected to be used in the study of p-adic cohomology in algebraic geometry; and also in the study of p-adic Banach spaces — by replacing the cumbersome "complete tensor product" of p-adic Banach spaces, with the more sophisticated "C-complete tensor product", discussed in this book. It is also not unlikely that the further study of these new invariants may well develop into a new branch of abstract mathematics - connected with commutative algebra, homological algebra, and algebraic topology.



Theory of Operator Algebras III

Theory of Operator Algebras III Author Masamichi Takesaki
ISBN-10 3540429131
Release 2002-11-01
Pages 548
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From the reviews: "These three bulky volumes [EMS 124, 125, 127] [...] provide an introduction to this rapidly developing theory. [...] These books can be warmly recommended to every graduate student who wants to become acquainted with this exciting branch of mathematics. Furthermore, they should be on the bookshelf of every researcher of the area." Acta Scientiarum Mathematicarum



Simplicial Homotopy Theory

Simplicial Homotopy Theory Author Paul G. Goerss
ISBN-10 3034601891
Release 2009-12-05
Pages 510
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Since the beginning of the modern era of algebraic topology, simplicial methods have been used systematically and effectively for both computation and basic theory. With the development of Quillen's concept of a closed model category and, in particular, a simplicial model category, this collection of methods has become the primary way to describe non-abelian homological algebra and to address homotopy-theoretical issues in a variety of fields, including algebraic K-theory. This book supplies a modern exposition of these ideas, emphasizing model category theoretical techniques. Discussed here are the homotopy theory of simplicial sets, and other basic topics such as simplicial groups, Postnikov towers, and bisimplicial sets. The more advanced material includes homotopy limits and colimits, localization with respect to a map and with respect to a homology theory, cosimplicial spaces, and homotopy coherence. Interspersed throughout are many results and ideas well-known to experts, but uncollected in the literature. Intended for second-year graduate students and beyond, this book introduces many of the basic tools of modern homotopy theory. An extensive background in topology is not assumed. Reviews: "... a book filling an obvious gap in the literature and the authors have done an excellent job on it. No monograph or expository paper has been published on this topic in the last twenty-eight years." - Analele Universitatii din Timisoara "... is clearly presented and a brief summary preceding every chapter is useful to the reader. The book should prove enlightening to a broad range of readers including prospective students and researchers who want to apply simplicial techniques for whatever reason." - Zentralblatt MATH "... they succeed. The book is an excellent account of simplicial homotopy theory from a modern point of view [...] The book is well written. [...] The book can be highly recommended to anybody who wants to learn and to apply simplicial techniques and/or the theory of (simplicial) closed model categories." - Mathematical Reviews



Strong Limit Theorems in Non Commutative Probability

Strong Limit Theorems in Non Commutative Probability Author R. Jajte
ISBN-10 9783540391395
Release 2007-01-05
Pages 156
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Strong Limit Theorems in Non Commutative Probability has been writing in one form or another for most of life. You can find so many inspiration from Strong Limit Theorems in Non Commutative Probability also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Strong Limit Theorems in Non Commutative Probability book for free.



Homological and Computational Methods in Commutative Algebra

Homological and Computational Methods in Commutative Algebra Author Aldo Conca
ISBN-10 9783319619439
Release 2017-11-16
Pages 256
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This volume collects contributions by leading experts in the area of commutative algebra related to the INdAM meeting “Homological and Computational Methods in Commutative Algebra” held in Cortona (Italy) from May 30 to June 3, 2016 . The conference and this volume are dedicated to Winfried Bruns on the occasion of his 70th birthday. In particular, the topics of this book strongly reflect the variety of Winfried Bruns’ research interests and his great impact on commutative algebra as well as its applications to related fields. The authors discuss recent and relevant developments in algebraic geometry, commutative algebra, computational algebra, discrete geometry and homological algebra. The book offers a unique resource, both for young and more experienced researchers seeking comprehensive overviews and extensive bibliographic references.



Undergraduate Commutative Algebra

Undergraduate Commutative Algebra Author Miles Reid
ISBN-10 0521458897
Release 1995-11-30
Pages 153
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In this well-written introduction to commutative algebra, the author shows the link between commutative ring theory and algebraic geometry. In addition to standard material, the book contrasts the methods and ideology of modern abstract algebra with concrete applications in algebraic geometry and number theory. Professor Reid begins with a discussion of modules and Noetherian rings before moving on to finite extensions and the Noether normalization. Sections on the nullstellensatz and rings of fractions precede sections on primary decomposition and normal integral domains. This book is ideal for anyone seeking a primer on commutative algebra.



C algebras of Homoclinic and Heteroclinic Structure in Expansive Dynamics

C  algebras of Homoclinic and Heteroclinic Structure in Expansive Dynamics Author Klaus Thomsen
ISBN-10 9780821846926
Release 2010-06-11
Pages 122
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The author unifies various constructions of $C^*$-algebras from dynamical systems, specifically, the dimension group construction of Krieger for shift spaces, the corresponding constructions of Wagoner and Boyle, Fiebig and Fiebig for countable state Markov shifts and one-sided shift spaces, respectively, and the constructions of Ruelle and Putnam for Smale spaces. The general setup is used to analyze the structure of the $C^*$-algebras arising from the homoclinic and heteroclinic equivalence relations in expansive dynamical systems, in particular, expansive group endomorphisms and automorphisms and generalized 1-solenoids. For these dynamical systems it is shown that the $C^*$-algebras are inductive limits of homogeneous or sub-homogeneous algebras with one-dimensional spectra.



Commutative Algebra

Commutative Algebra Author Marco Fontana
ISBN-10 144196990X
Release 2010-09-29
Pages 492
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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.



A Course in Commutative Algebra

A Course in Commutative Algebra Author Gregor Kemper
ISBN-10 3642035450
Release 2010-12-02
Pages 248
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This textbook offers a thorough, modern introduction into commutative algebra. It is intented mainly to serve as a guide for a course of one or two semesters, or for self-study. The carefully selected subject matter concentrates on the concepts and results at the center of the field. The book maintains a constant view on the natural geometric context, enabling the reader to gain a deeper understanding of the material. Although it emphasizes theory, three chapters are devoted to computational aspects. Many illustrative examples and exercises enrich the text.