The Separable Galois Theory of Commutative Rings (Chapman & Hall/crc Pure and Applied Mathematics) （2ND）

Magid, Andy R.

Chapman & Hall/CRC（2014/07発売）

• 製本 Hardcover:ハードカバー版／ページ数 184 p.
• 言語 ENG
• 商品コード 9781482208054
• DDC分類 664.68

Full Description

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.

Contents

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.