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Separable Algebras
 
Timothy J. Ford Florida Atlantic University, Boca Raton, FL
Separable Algebras
Hardcover ISBN:  978-1-4704-3770-1
Product Code:  GSM/183
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
eBook ISBN:  978-1-4704-4230-9
Product Code:  GSM/183.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Hardcover ISBN:  978-1-4704-3770-1
eBook: ISBN:  978-1-4704-4230-9
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
Separable Algebras
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Separable Algebras
Timothy J. Ford Florida Atlantic University, Boca Raton, FL
Hardcover ISBN:  978-1-4704-3770-1
Product Code:  GSM/183
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
eBook ISBN:  978-1-4704-4230-9
Product Code:  GSM/183.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Hardcover ISBN:  978-1-4704-3770-1
eBook ISBN:  978-1-4704-4230-9
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 Details
     
     
    Graduate Studies in Mathematics
    Volume: 1832017; 637 pp
    MSC: 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.

    Readership

    Graduate students and researchers interested in algebra.

  • Table of Contents
     
     
    • Chapters
    • Background material on rings and modules
    • Modules over commutative rings
    • The Wedderburn-Artin 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
  • Reviews
     
     
    • The book is neatly arranged. It can be used as a textbook for self-study 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, well-chosen examples, calculations, and sets of exercises in each chapter, which makes this book an excellent textbook for self-study or for a topics course on separable algebras.

      Felipe Zaldivar, MAA Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1832017; 637 pp
MSC: 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.

Readership

Graduate students and researchers interested in algebra.

  • Chapters
  • Background material on rings and modules
  • Modules over commutative rings
  • The Wedderburn-Artin 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 self-study 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, well-chosen examples, calculations, and sets of exercises in each chapter, which makes this book an excellent textbook for self-study or for a topics course on separable algebras.

    Felipe Zaldivar, MAA Reviews
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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