Galois Theories
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.
1100938012
Galois Theories
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.
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Galois Theories

Galois Theories

Galois Theories

Galois Theories

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: 02/22/2001
Series: Cambridge Studies in Advanced Mathematics , #72
Pages: 356
Product dimensions: 6.18(w) x 9.33(h) x 0.94(d)

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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