Hardcover ISBN:  9781470437701 
Product Code:  GSM/183 
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AMS Member Price:  $108.00 
eBook ISBN:  9781470442309 
Product Code:  GSM/183.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9781470437701 
eBook: ISBN:  9781470442309 
Product Code:  GSM/183.B 
List Price:  $220.00 $177.50 
MAA Member Price:  $198.00 $159.75 
AMS Member Price:  $176.00 $142.00 
Hardcover ISBN:  9781470437701 
Product Code:  GSM/183 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
eBook ISBN:  9781470442309 
Product Code:  GSM/183.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9781470437701 
eBook ISBN:  9781470442309 
Product Code:  GSM/183.B 
List Price:  $220.00 $177.50 
MAA Member Price:  $198.00 $159.75 
AMS Member Price:  $176.00 $142.00 

Book DetailsGraduate Studies in MathematicsVolume: 183; 2017; 637 ppMSC: Primary 16; 15; 13; 14
This book presents a comprehensive introduction to the theory of separable algebras over commutative rings. After a thorough introduction to the general theory, the fundamental roles played by separable algebras are explored. For example, Azumaya algebras, the henselization of local rings, and Galois theory are rigorously introduced and treated. Interwoven throughout these applications is the important notion of étale algebras. Essential connections are drawn between the theory of separable algebras and Morita theory, the theory of faithfully flat descent, cohomology, derivations, differentials, reflexive lattices, maximal orders, and class groups.
The text is accessible to graduate students who have finished a first course in algebra, and it includes necessary foundational material, useful exercises, and many nontrivial examples.
ReadershipGraduate students and researchers interested in algebra.

Table of Contents

Chapters

Background material on rings and modules

Modules over commutative rings

The WedderburnArtin theorem

Separable algebras, definition and first properties

Background material on homological algebra

The divisor class group

Azumaya algebras, I

Derivations, differentials and separability

Étale algebras

Henselization and splitting rings

Azumaya algebras, II

Galois extensions of commutative rings

Crossed products and Galois cohomology

Further topics


Additional Material

Reviews

The book is neatly arranged. It can be used as a textbook for selfstudy and as a reference text for most of the topics related to separability...It will be a valuable resource for students and researchers and has the potential to be a standard reference on separable algebras for many years.
Wolfgang Rump, Mathematical Reviews 
The thorough and comprehensive treatment of separable, Azumaya, and tale algebras, Hensel rings, the Galois theory of rings, and Galois cohomology of rings makes the book under review an indispensable reference for the graduate student interested in these topics. As an added bonus, the book comes with a rich, 155 item, bibliography, wellchosen examples, calculations, and sets of exercises in each chapter, which makes this book an excellent textbook for selfstudy or for a topics course on separable algebras.
Felipe Zaldivar, MAA Reviews


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This book presents a comprehensive introduction to the theory of separable algebras over commutative rings. After a thorough introduction to the general theory, the fundamental roles played by separable algebras are explored. For example, Azumaya algebras, the henselization of local rings, and Galois theory are rigorously introduced and treated. Interwoven throughout these applications is the important notion of étale algebras. Essential connections are drawn between the theory of separable algebras and Morita theory, the theory of faithfully flat descent, cohomology, derivations, differentials, reflexive lattices, maximal orders, and class groups.
The text is accessible to graduate students who have finished a first course in algebra, and it includes necessary foundational material, useful exercises, and many nontrivial examples.
Graduate students and researchers interested in algebra.

Chapters

Background material on rings and modules

Modules over commutative rings

The WedderburnArtin theorem

Separable algebras, definition and first properties

Background material on homological algebra

The divisor class group

Azumaya algebras, I

Derivations, differentials and separability

Étale algebras

Henselization and splitting rings

Azumaya algebras, II

Galois extensions of commutative rings

Crossed products and Galois cohomology

Further topics

The book is neatly arranged. It can be used as a textbook for selfstudy and as a reference text for most of the topics related to separability...It will be a valuable resource for students and researchers and has the potential to be a standard reference on separable algebras for many years.
Wolfgang Rump, Mathematical Reviews 
The thorough and comprehensive treatment of separable, Azumaya, and tale algebras, Hensel rings, the Galois theory of rings, and Galois cohomology of rings makes the book under review an indispensable reference for the graduate student interested in these topics. As an added bonus, the book comes with a rich, 155 item, bibliography, wellchosen examples, calculations, and sets of exercises in each chapter, which makes this book an excellent textbook for selfstudy or for a topics course on separable algebras.
Felipe Zaldivar, MAA Reviews