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  3. Corings and Comodules
  • Cited by 165
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    • Publisher:
      Cambridge University Press
      Publication date:
      10 August 2009
      15 September 2003
      ISBN:
      9780511546495
      9780521539319
      DOI:
      https://doi.org/10.1017/CBO9780511546495
      Dimensions:
      Weight & Pages:
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.671kg, 490 Pages
      • Subjects:
      Mathematics (general), Mathematics, Algebra
      Series:
      London Mathematical Society Lecture Note Series (309)
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    Subjects:
    Mathematics (general), Mathematics, Algebra
    Series:
    London Mathematical Society Lecture Note Series (309)
    Information

    Book description

    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.

    Reviews

    ‘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.’

    Source: Zentralblatt MATH

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