Modules And Comodules
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Modules And Comodules
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Author : Tomasz Brzezinski
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-06-26
Modules And Comodules written by Tomasz Brzezinski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-26 with Mathematics categories.
The 23 articles in this volume encompass the proceedings of the International Conference on Modules and Comodules held in Porto (Portugal) in 2006. The conference was dedicated to Robert Wisbauer on the occasion of his 65th birthday. These articles reflect Professor Wisbauer's wide interests and give an overview of different fields related to module theory. While some of these fields have a long tradition, others represented here have emerged in recent years.
Corings And Comodules
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Author : Tomasz Brzezinski
language : en
Publisher: Cambridge University Press
Release Date : 2003-09-15
Corings And Comodules written by Tomasz Brzezinski and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-09-15 with Mathematics categories.
This is the first extensive treatment of the theory of corings and their comodules. In the first part, the module-theoretic aspects of coalgebras over commutative rings are described. Corings are then defined as coalgebras over non-commutative rings. Topics covered include module-theoretic aspects of corings, such as the relation of comodules to special subcategories of the category of modules (sigma-type categories), connections between corings and extensions of rings, properties of new examples of corings associated to entwining structures, generalisations of bialgebras such as bialgebroids and weak bialgebras, and the appearance of corings in non-commutative geometry.
Homological Algebra Of Semimodules And Semicontramodules
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Author : Leonid Positselski
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-02
Homological Algebra Of Semimodules And Semicontramodules written by Leonid Positselski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-02 with Mathematics categories.
This book provides comprehensive coverage on semi-infinite homology and cohomology of associative algebraic structures. It features rich representation-theoretic and algebro-geometric examples and applications.
Two Kinds Of Derived Categories Koszul Duality And Comodule Contramodule Correspondence
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Author : Leonid Positselski
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Two Kinds Of Derived Categories Koszul Duality And Comodule Contramodule Correspondence written by Leonid Positselski and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
"July 2011, volume 212, number 996 (first of 4 numbers)."
Frobenius And Separable Functors For Generalized Module Categories And Nonlinear Equations
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Author : Stefaan Caenepeel
language : en
Publisher: Springer
Release Date : 2004-10-13
Frobenius And Separable Functors For Generalized Module Categories And Nonlinear Equations written by Stefaan Caenepeel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-13 with Mathematics categories.
Doi-Koppinen Hopf modules and entwined modules unify various kinds of modules that have been intensively studied over the past decades, such as Hopf modules, graded modules, Yetter-Drinfeld modules. The book presents a unified theory, with focus on categorical concepts generalizing the notions of separable and Frobenius algebras, and discussing relations with smash products, Galois theory and descent theory. Each chapter of Part II is devoted to a particular nonlinear equation. The exposé is organized in such a way that the analogies between the four are clear: the quantum Yang-Baxter equation is related to Yetter-Drinfeld modules, the pentagon equation to Hopf modules, and the Long equation to Long dimodules. The Frobenius-separability equation provides a new viewpoint to Frobenius and separable algebras.
Rings Modules Algebras And Abelian Groups
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Author : Alberto Facchini
language : en
Publisher: CRC Press
Release Date : 2020-02-10
Rings Modules Algebras And Abelian Groups written by Alberto Facchini and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-10 with Mathematics categories.
Rings, Modules, Algebras, and Abelian Groups summarizes the proceedings of a recent algebraic conference held at Venice International University in Italy. Surveying the most influential developments in the field, this reference reviews the latest research on Abelian groups, algebras and their representations, module and ring theory, and topological
Relative Nonhomogeneous Koszul Duality
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Author : Leonid Positselski
language : en
Publisher: Springer Nature
Release Date : 2022-02-10
Relative Nonhomogeneous Koszul Duality written by Leonid Positselski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-10 with Mathematics categories.
This research monograph develops the theory of relative nonhomogeneous Koszul duality. Koszul duality is a fundamental phenomenon in homological algebra and related areas of mathematics, such as algebraic topology, algebraic geometry, and representation theory. Koszul duality is a popular subject of contemporary research. This book, written by one of the world's leading experts in the area, includes the homogeneous and nonhomogeneous quadratic duality theory over a nonsemisimple, noncommutative base ring, the Poincare–Birkhoff–Witt theorem generalized to this context, and triangulated equivalences between suitable exotic derived categories of modules, curved DG comodules, and curved DG contramodules. The thematic example, meaning the classical duality between the ring of differential operators and the de Rham DG algebra of differential forms, involves some of the most important objects of study in the contemporary algebraic and differential geometry. For the first time in the history of Koszul duality the derived D-\Omega duality is included into a general framework. Examples highly relevant for algebraic and differential geometry are discussed in detail.
Handbook Of Algebra
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Author : M. Hazewinkel
language : en
Publisher: Elsevier
Release Date : 2009-07-08
Handbook Of Algebra written by M. Hazewinkel and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-08 with Mathematics categories.
Algebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these have been named and many more could (and perhaps should) have a name or a convenient designation. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. If this happens, one should be able to find enough information in this Handbook to judge if it is worthwhile to pursue the quest. In addition to the primary information given in the Handbook, there are references to relevant articles, books or lecture notes to help the reader. An excellent index has been included which is extensive and not limited to definitions, theorems etc. The Handbook of Algebra will publish articles as they are received and thus the reader will find in this third volume articles from twelve different sections. The advantages of this scheme are two-fold: accepted articles will be published quickly and the outline of the Handbook can be allowed to evolve as the various volumes are published. A particularly important function of the Handbook is to provide professional mathematicians working in an area other than their own with sufficient information on the topic in question if and when it is needed.- Thorough and practical source of information - Provides in-depth coverage of new topics in algebra - Includes references to relevant articles, books and lecture notes
More Concise Algebraic Topology
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Author : J. P. May
language : en
Publisher: University of Chicago Press
Release Date : 2012-02
More Concise Algebraic Topology written by J. P. May and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02 with Mathematics categories.
With firm foundations dating only from the 1950s, algebraic topology is a relatively young area of mathematics. There are very few textbooks that treat fundamental topics beyond a first course, and many topics now essential to the field are not treated in any textbook. J. Peter May’s A Concise Course in Algebraic Topology addresses the standard first course material, such as fundamental groups, covering spaces, the basics of homotopy theory, and homology and cohomology. In this sequel, May and his coauthor, Kathleen Ponto, cover topics that are essential for algebraic topologists and others interested in algebraic topology, but that are not treated in standard texts. They focus on the localization and completion of topological spaces, model categories, and Hopf algebras. The first half of the book sets out the basic theory of localization and completion of nilpotent spaces, using the most elementary treatment the authors know of. It makes no use of simplicial techniques or model categories, and it provides full details of other necessary preliminaries. With these topics as motivation, most of the second half of the book sets out the theory of model categories, which is the central organizing framework for homotopical algebra in general. Examples from topology and homological algebra are treated in parallel. A short last part develops the basic theory of bialgebras and Hopf algebras.
Homotopy Theory Relations With Algebraic Geometry Group Cohomology And Algebraic K Theory
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Author : Paul Gregory Goerss
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Homotopy Theory Relations With Algebraic Geometry Group Cohomology And Algebraic K Theory written by Paul Gregory Goerss and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
As part of its series of Emphasis Years in Mathematics, Northwestern University hosted an International Conference on Algebraic Topology. The purpose of the conference was to develop new connections between homotopy theory and other areas of mathematics. This proceedings volume grew out of that event. Topics discussed include algebraic geometry, cohomology of groups, algebraic $K$-theory, and $\mathbb{A 1$ homotopy theory. Among the contributors to the volume were Alejandro Adem,Ralph L. Cohen, Jean-Louis Loday, and many others. The book is suitable for graduate students and research mathematicians interested in homotopy theory and its relationship to other areas of mathematics.