Galois Theories by Francis Borceux, George Janelidze - 9780521070416

Galois TheoriesAuthor(s): Francis Borceux, George Janelidze\nFormat: Paperback\nPublisher: Cambridge University Press, United Kingdom\nImprint: Cambridge University Press\nISBN-13: 9780521070416, 978-0521070416\nSynopsis\nStarting from the classical finite-dimensional Galois theory of fields, this book develops Galois theory in a much more general context, presenting work by Grothendieck in terms of separable algebras and then proceeding to the infinite-dimensional case, which requires considering topological Galois groups. In the core of the book, the authors first formalize the categorical context in which a general Galois theorem holds, and then give applications to Galois theory for commutative rings, central extensions of groups, the topological theory of covering maps and a Galois theorem for toposes. The book is designed to be accessible to a wide audience: the prerequisites are first courses in algebra and general topology, together with some familiarity with the categorical .