Galois Theories

Galois Theories

by Francis Borceux, George Janelidze, George Janelidze
     
 

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ISBN-10: 0521803098

ISBN-13: 9780521803090

Pub. Date: 05/28/2003

Publisher: Cambridge University Press

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

Overview

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.

Product Details

ISBN-13:
9780521803090
Publisher:
Cambridge University Press
Publication date:
05/28/2003
Series:
Cambridge Studies in Advanced Mathematics Series, #72
Pages:
356
Product dimensions:
5.98(w) x 8.98(h) x 0.94(d)

Related Subjects

Table of Contents

Introduction; 1. Classical Galois theory; 2. Galois theory of Grothendieck; 3. Infinitary Galois theory; 4. Categorical Galois theory of commutative rings; 5. Categorical Galois theorem and factorization systems; 6. Covering maps; 7. Non-Galoisian Galois theory; Appendix; Bibliography; Index.

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