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, 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 notions of limit and adjoint functors. The first chapters are accessible to advanced undergraduates, with later ones at a graduate level. For all algebraists and category theorists this book will be a rewarding read.

About this title

Review:

Review of the hardback: 'This book is a beautiful presentation of Janelidze's general categorical Galois theory ... a rewarding read.' László Márki, Acta Sci. Math.

Review of the hardback: '... highly recommended or anyone wishing to learn the mathematical side of category theory (rather than its computer-science aspect) ... I enjoyed reading it very much.' Proceedings of the Edinburgh Mathematical Society

Review of the hardback: 'A comprehensive account, which may well deepen one's understanding of the classical case.' Mathematika

Book Description:

Develops Galois theory in a much more general context than the undegraduate-style Galois theory of fields. In particular, the relationship with category theory is emphasized. Treats work by leading researchers in the field, and includes a comprehensive bibliography and index. Will be interesting for algebraists and category theorists.

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