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Author: Tomasz Brzezinski
Publisher: Cambridge University Press
ISBN: 9780521539319
Category : Mathematics
Languages : en
Pages : 492
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Book Description
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.
Author: Tomasz Brzezinski
Publisher: Cambridge University Press
ISBN: 9780521539319
Category : Mathematics
Languages : en
Pages : 492
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Book Description
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.
Author: Tomasz Brzezinski
Publisher: Springer Science & Business Media
ISBN: 3764387424
Category : Mathematics
Languages : en
Pages : 355
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Book Description
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.
Author: Heulwen Rankin
Publisher:
ISBN: 9780494268810
Category : Comodules
Languages : en
Pages : 120
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Book Description
Author: M. Hazewinkel
Publisher: Elsevier
ISBN: 0080932819
Category : Mathematics
Languages : en
Pages : 637
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Book Description
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
Author: Stefaan Caenepeel
Publisher: Springer
ISBN: 3540480420
Category : Mathematics
Languages : en
Pages : 359
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Book Description
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.
Author: Jianlong Chen
Publisher: World Scientific
ISBN: 9814479705
Category : Mathematics
Languages : en
Pages : 335
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Book Description
The selected papers in this volume cover all the most important areas of ring theory and module theory such as classical ring theory, representation theory, the theory of quantum groups, the theory of Hopf algebras, the theory of Lie algebras and Abelian group theory. The review articles, written by specialists, provide an excellent overview of the various areas of ring and module theory — ideal for researchers looking for a new or related field of study. Also included are original articles showing the trend of current research.
Author: Stefaan Caenepeel
Publisher: CRC Press
ISBN: 0429530072
Category : Mathematics
Languages : en
Pages : 348
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Book Description
This comprehensive reference summarizes the proceedings and keynote presentations from a recent conference held in Brussels, Belgium. Offering 1155 display equations, this volume contains original research and survey papers as well as contributions from world-renowned algebraists. It focuses on new results in classical Hopf algebras as well as the
Author: Leonid Positselski
Publisher: Springer Science & Business Media
ISBN: 303460436X
Category : Mathematics
Languages : en
Pages : 364
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Book Description
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.
Author: George Janelidze, Bodo Pareigis, and Walter Tholen
Publisher: American Mathematical Soc.
ISBN: 9780821871478
Category :
Languages : en
Pages : 588
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Book Description
Author: L. El Kaoutit
Publisher:
ISBN:
Category :
Languages : en
Pages : 15
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Book Description
While semisimple artinian rings and semisimple coalgebras over a field can be described in terms of matrices (either matrix ring over division rings or comatrix coalgebras over the ground field), semisimple corings seem to have a more intrincated structure in general. It turns out that some well-known properties of semisimple rings or coalgebras, which are immediately deduced from the aforementioned structure, are not evident over a (left) semi-simple coring. For instance, it is not evident that the notion of semi-simple coring is left-right symmetric. To be precise, if every left comodule decomposes a a direct sum of simple comodules, do the right comodules have such a decomposition? In other words, is every left semi-simple coring a right semi-simple coring? We develope the basic essentials for a theory of semi-simple corings, giving a positive answer for the last question, as well as some information about the structure of semi-simple corings.
