Galois Theories (Cambridge Studies in Advanced Mathematics, Series Number 72) - Softcover

Borceux, Francis

Softcover

ISBN 10: 0521070414 ISBN 13: 9780521070416

Publisher: Cambridge University Press, 2008

Synopsis

Starting from the classical finite-dimensional Galois theory of fields, this book develops Galois theory in a much more general context. 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 notions of limit and adjoint functors. For all algebraists and category theorists this book will be a rewarding read.

About this title

Book Description:

This book develops the basic structure of Galois theory treated in standard undergraduate courses in a much more general context, including the infinite-dimensional case and in more general algebraic structures. In particular, the relationship with category theory is emphasised. Much of the material, recent work by leading researchers in the field, appears here for the first time in book form. The first chapters are at an advanced undergraduate level, the later ones at a graduate level; the book will be especially interesting for the algebra and category theory communities.

Review:

"This is a clearly written and readable book covering a lot of interesting and important material, and effectively leading the reader through increasing levels of generality and abstraction." Mathematical Review

About this edition

• Publisher: Cambridge University Press
• Publication date: 2008
• ISBN 10: 0521070414
• ISBN 13: 9780521070416
• Binding: Paperback
• Edition number: 1
• Number of pages: 356