Corings and comodules are fundamental algebraic structures, which can be thought of as both dualisations and generalisations of rings and modules. Introduced by Sweedler in 1975, only recently they have been shown to have far reaching applications ranging from the category theory including differential graded categories through classical and Hopf-type module theory to non-commutative geometry and mathematical physics. 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.
- First book devoted to the rapidly developing theory of corings
- Provides connections with other branches of pure mathematics and mathematical physics
- Incorporates most recent developments
- Developing the module-theoretic aspects of corings it extends the theory of Hopf algebras and quantum groups
- Self-contained exposition with expanded appendices, which makes it suitable for graduate students
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Reviews & endorsements
'This book is clearly written and it is the first account of what is known about coring theory. The book can be used as a textbook for a very good graduate course in coalgebras and corings. It will also help to develop and increase the interest in the theory of corings. I also expect that it will be a standard reference for corings in the future.' Zentralblatt MATH

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Product details
- Date Published: September 2003
- format: Paperback
- isbn: 9780521539319
- length: 490 pages
- dimensions: 230 x 153 x 26 mm
- weight: 0.671kg
- availability: Available
Table of Contents
Preface
Notations
1. Coalgebras and comodules
2. Bialgebras and hopf algebras
3. Corings and comodules
4. Corings and extensions of rings
5. Corings and entwining structures
6. Weak corings and entwining
Appendix.
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