by Francine Stock (Author)
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.
Format: Hardcover
Pages: 256
Edition: First Edition
Publisher: Chatto & Windus
Published: 01 Aug 2002
ISBN 10: 0701173424
ISBN 13: 9780701173425
Book Overview: A brilliantly evocative, poignant and sharply funny novel about life, love and marriage at that pivotal moment in 1961 when the man-made world of the Fifties was about to change, for women like Patsy in particular...