Galois Theories (Cambridge Studies in Advanced Mathematics)

出版者:Cambridge University Press

作者:Francis Borceux

页数:356

出版时间:2008-07-31

价格:USD 65.00

装帧:Paperback

isbn号码:9780521070416

丛书系列:Cambridge Studies in Advanced Mathematics

具体描述

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.

目录信息

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
· · · · · · (收起)

用户评价

非常精炼的参考书，从古典Galois理论开始，发展出交换代数与交换环的Galois理论，范畴Galois理论是核心，最后以Topos理论结尾，对范畴论的要求比较高，不把GTM5打通读起来很费力，我也是先了解一个框架，有些内容以后再慢慢消化。

非常精炼的参考书，从古典Galois理论开始，发展出交换代数与交换环的Galois理论，范畴Galois理论是核心，最后以Topos理论结尾，对范畴论的要求比较高，不把GTM5打通读起来很费力，我也是先了解一个框架，有些内容以后再慢慢消化。

非常精炼的参考书，从古典Galois理论开始，发展出交换代数与交换环的Galois理论，范畴Galois理论是核心，最后以Topos理论结尾，对范畴论的要求比较高，不把GTM5打通读起来很费力，我也是先了解一个框架，有些内容以后再慢慢消化。

非常精炼的参考书，从古典Galois理论开始，发展出交换代数与交换环的Galois理论，范畴Galois理论是核心，最后以Topos理论结尾，对范畴论的要求比较高，不把GTM5打通读起来很费力，我也是先了解一个框架，有些内容以后再慢慢消化。

非常精炼的参考书，从古典Galois理论开始，发展出交换代数与交换环的Galois理论，范畴Galois理论是核心，最后以Topos理论结尾，对范畴论的要求比较高，不把GTM5打通读起来很费力，我也是先了解一个框架，有些内容以后再慢慢消化。