The Separable Galois Theory of Commutative Rings, Second Edition provides a complete and self-contained account of the Galois theory of commutative rings from the viewpoint of categorical classification theorems and using solely the techniques of commutative algebra. Along with updating nearly every result and explanation, this edition contains a new chapter on the theory of separable algebras.
The book develops the notion of commutative separable algebra over a given commutative ring and explains how to construct an equivalent category of profinite spaces on which a profinite groupoid acts. It explores how the connection between the categories depends on the construction of a suitable separable closure of the given ring, which in turn depends on certain notions in profinite topology. The book also discusses how to handle rings with infinitely many idempotents using profinite topological spaces and other methods.
By:
Andy R. Magid (The University of Oklahoma Norman USA) Imprint: Chapman & Hall/CRC Country of Publication: United States Edition: 2nd edition Volume: 307 Dimensions:
Height: 234mm,
Width: 156mm,
Spine: 15mm
Weight: 385g ISBN:9781482208054 ISBN 10: 1482208059 Series:Chapman & Hall/CRC Pure and Applied Mathematics Pages: 184 Publication Date:14 July 2014 Audience:
College/higher education
,
Professional and scholarly
,
A / AS level
,
Further / Higher Education
Format:Hardback Publisher's Status: Active
Separability. Idempotents and Profinite Spaces. The Boolean Spectrum. Galois Theory over a Connected Base. Separable Closure and the Fundamental Groupoid. Categorical Galois Theory and the Galois Correspondence. Index.
Andy R. Magid
Reviews for The Separable Galois Theory of Commutative Rings
This book provides a complete and self-contained account of the Galois theory of commutative rings ... -Nikolay I. Kryuchkov, Zentralblatt MATH 1298