The Separable Galois Theory of Commutative Rings

2nd Edition

Andy R. Magid

Chapman and Hall/CRC
Published July 14, 2014
Reference - 184 Pages
ISBN 9781482208054 - CAT# K21564
Series: Chapman & Hall/CRC Pure and Applied Mathematics

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Summary

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.