Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
Hopf Algebras and Galois Module Theory
 
Lindsay N. Childs University at Albany, Albany, NY
Cornelius Greither Universität der Bundeswehr München, Neubiberg, Germany
Kevin P. Keating University of Florida, Gainesville, FL
Alan Koch Agnes Scott College, Decatur, GA
Timothy Kohl Boston University, Boston, MA
Paul J. Truman Keele University, Staffordshire, United Kingdom
Robert G. Underwood Auburn University at Montgomery, Montgomery, AL
Hopf Algebras and Galois Module Theory
Softcover ISBN:  978-1-4704-6516-2
Product Code:  SURV/260
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
eBook ISBN:  978-1-4704-6737-1
Product Code:  SURV/260.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-1-4704-6516-2
eBook: ISBN:  978-1-4704-6737-1
Product Code:  SURV/260.B
List Price: $250.00 $187.50
MAA Member Price: $225.00 $168.75
AMS Member Price: $200.00 $150.00
Hopf Algebras and Galois Module Theory
Click above image for expanded view
Hopf Algebras and Galois Module Theory
Lindsay N. Childs University at Albany, Albany, NY
Cornelius Greither Universität der Bundeswehr München, Neubiberg, Germany
Kevin P. Keating University of Florida, Gainesville, FL
Alan Koch Agnes Scott College, Decatur, GA
Timothy Kohl Boston University, Boston, MA
Paul J. Truman Keele University, Staffordshire, United Kingdom
Robert G. Underwood Auburn University at Montgomery, Montgomery, AL
Softcover ISBN:  978-1-4704-6516-2
Product Code:  SURV/260
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
eBook ISBN:  978-1-4704-6737-1
Product Code:  SURV/260.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-1-4704-6516-2
eBook ISBN:  978-1-4704-6737-1
Product Code:  SURV/260.B
List Price: $250.00 $187.50
MAA Member Price: $225.00 $168.75
AMS Member Price: $200.00 $150.00
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 2602021; 311 pp
    MSC: Primary 16; 11; Secondary 12; 20

    Hopf algebras have been shown to play a natural role in studying questions of integral module structure in extensions of local or global fields. This book surveys the state of the art in Hopf-Galois theory and Hopf-Galois module theory and can be viewed as a sequel to the first author's book, Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory, which was published in 2000.

    The book is divided into two parts. Part I is more algebraic and focuses on Hopf-Galois structures on Galois field extensions, as well as the connection between this topic and the theory of skew braces. Part II is more number theoretical and studies the application of Hopf algebras to questions of integral module structure in extensions of local or global fields.

    Graduate students and researchers with a general background in graduate-level algebra, algebraic number theory, and some familiarity with Hopf algebras will appreciate the overview of the current state of this exciting area and the suggestions for numerous avenues for further research and investigation.

    Readership

    Graduate students and researchers interested in Hopf algebras.

  • Table of Contents
     
     
    • Chapters
    • Introduction: What is this book about?
    • Hopf-Galois extensions
    • Hopf-Galois structures on Galois extensions of fields, regular subgroups, and skew braces
    • (Non)-existence results on Hopf-Galois structures
    • Hopf-Galois structures arising from fixed point free pairs of homomorphisms
    • Quantitative results
    • Enumeration of Hopf-Galois structures on Galois extenion of degree $mp$
    • On the Galois correspondence for Hopf-Galois structures
    • Normality in Hopf-Galois extensions
    • Descent theory, and the structure of Hopf algebras acting on separable field extensions
    • Hopf-Galois actions on purely inseparable extensions
    • Hopf-Galois module theory
    • Hopf-Galois module theory
    • Hopf orders in group rings
    • Ramification theory for separable extensions of local fields
    • Stable and semistable Hopf-Galois extensions
    • Hopf-Galois scaffolds
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2602021; 311 pp
MSC: Primary 16; 11; Secondary 12; 20

Hopf algebras have been shown to play a natural role in studying questions of integral module structure in extensions of local or global fields. This book surveys the state of the art in Hopf-Galois theory and Hopf-Galois module theory and can be viewed as a sequel to the first author's book, Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory, which was published in 2000.

The book is divided into two parts. Part I is more algebraic and focuses on Hopf-Galois structures on Galois field extensions, as well as the connection between this topic and the theory of skew braces. Part II is more number theoretical and studies the application of Hopf algebras to questions of integral module structure in extensions of local or global fields.

Graduate students and researchers with a general background in graduate-level algebra, algebraic number theory, and some familiarity with Hopf algebras will appreciate the overview of the current state of this exciting area and the suggestions for numerous avenues for further research and investigation.

Readership

Graduate students and researchers interested in Hopf algebras.

  • Chapters
  • Introduction: What is this book about?
  • Hopf-Galois extensions
  • Hopf-Galois structures on Galois extensions of fields, regular subgroups, and skew braces
  • (Non)-existence results on Hopf-Galois structures
  • Hopf-Galois structures arising from fixed point free pairs of homomorphisms
  • Quantitative results
  • Enumeration of Hopf-Galois structures on Galois extenion of degree $mp$
  • On the Galois correspondence for Hopf-Galois structures
  • Normality in Hopf-Galois extensions
  • Descent theory, and the structure of Hopf algebras acting on separable field extensions
  • Hopf-Galois actions on purely inseparable extensions
  • Hopf-Galois module theory
  • Hopf-Galois module theory
  • Hopf orders in group rings
  • Ramification theory for separable extensions of local fields
  • Stable and semistable Hopf-Galois extensions
  • Hopf-Galois scaffolds
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
You may be interested in...
Please select which format for which you are requesting permissions.