The Separable Galois Theory of Commutative Rings
The Separable Galois Theory of Commutative Rings

Author: Andy R. Magid

Publisher: CRC Press

Published: 2014-07-14

Total Pages: 184

ISBN-13: 1482208067

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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 n

Cyclic Galois Extensions of Commutative Rings
Cyclic Galois Extensions of Commutative Rings

Author: Cornelius Greither

Publisher: Springer

Published: 2006-11-15

Total Pages: 155

ISBN-13: 3540475397

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The structure theory of abelian extensions of commutative rings is a subjectwhere commutative algebra and algebraic number theory overlap. This exposition is aimed at readers with some background in either of these two fields. Emphasis is given to the notion of a normal basis, which allows one to view in a well-known conjecture in number theory (Leopoldt's conjecture) from a new angle. Methods to construct certain extensions quite explicitly are also described at length.

An Introduction to Galois Cohomology and its Applications
An Introduction to Galois Cohomology and its Applications

Author: Grégory Berhuy

Publisher: Cambridge University Press

Published: 2010-09-09

Total Pages: 328

ISBN-13: 1139490885

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This is the first detailed elementary introduction to Galois cohomology and its applications. The introductory section is self-contained and provides the basic results of the theory. Assuming only a minimal background in algebra, the main purpose of this book is to prepare graduate students and researchers for more advanced study.

Brauer Groups and the Cohomology of Graded Rings
Brauer Groups and the Cohomology of Graded Rings

Author: Stefaan Caenepeel

Publisher: CRC Press

Published: 2020-08-26

Total Pages: 280

ISBN-13: 1000103781

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This book introduces various notions defined in graded terms extending the notions most frequently used as basic ingredients in the theory of Azumaya algebras: separability and Galois extensions of commutative rings, crossed products and Galois cohomology, Picard groups, and the Brauer group.