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!
Faithfully Quadratic Rings
 
M. Dickmann Institut de Mathématiques de Jussieu-Paris Rive Gauche, France
F. Miraglia University of São Paulo, Brasil
Faithfully Quadratic Rings
eBook ISBN:  978-1-4704-2629-3
Product Code:  MEMO/238/1128.E
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
Faithfully Quadratic Rings
Click above image for expanded view
Faithfully Quadratic Rings
M. Dickmann Institut de Mathématiques de Jussieu-Paris Rive Gauche, France
F. Miraglia University of São Paulo, Brasil
eBook ISBN:  978-1-4704-2629-3
Product Code:  MEMO/238/1128.E
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2382015; 129 pp
    MSC: Primary 11; 12; 03; 06; 46; 54;

    In this monograph the authors extend the classical algebraic theory of quadratic forms over fields to diagonal quadratic forms with invertible entries over broad classes of commutative, unitary rings where \(-1\) is not a sum of squares and \(2\) is invertible. They accomplish this by:

    (1) Extending the classical notion of matrix isometry of forms to a suitable notion of \(T\)-isometry, where \(T\) is a preorder of the given ring, \(A\), or \(T = A^2\).

    (2) Introducing in this context three axioms expressing simple properties of (value) representation of elements of the ring by quadratic forms, well-known to hold in the field case.

  • Table of Contents
     
     
    • Chapters
    • Preface
    • 1. Basic Concepts
    • 2. Rings and Special Groups
    • 3. The Notion of T-Faithfully Quadratic Ring. Some Basic Consequences
    • 4. Idempotents, Products and T-isometry
    • 5. First-Order Axioms for Quadratic Faithfulness
    • 6. Rings with Many Units
    • 7. Transversality of Representation in p-rings with Bounded Inversion
    • 8. Reduced $f$-Rings
    • 9. Strictly Representable Rings
    • 10. Quadratic Form Theory over Faithfully Quadratic Rings
  • 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: 2382015; 129 pp
MSC: Primary 11; 12; 03; 06; 46; 54;

In this monograph the authors extend the classical algebraic theory of quadratic forms over fields to diagonal quadratic forms with invertible entries over broad classes of commutative, unitary rings where \(-1\) is not a sum of squares and \(2\) is invertible. They accomplish this by:

(1) Extending the classical notion of matrix isometry of forms to a suitable notion of \(T\)-isometry, where \(T\) is a preorder of the given ring, \(A\), or \(T = A^2\).

(2) Introducing in this context three axioms expressing simple properties of (value) representation of elements of the ring by quadratic forms, well-known to hold in the field case.

  • Chapters
  • Preface
  • 1. Basic Concepts
  • 2. Rings and Special Groups
  • 3. The Notion of T-Faithfully Quadratic Ring. Some Basic Consequences
  • 4. Idempotents, Products and T-isometry
  • 5. First-Order Axioms for Quadratic Faithfulness
  • 6. Rings with Many Units
  • 7. Transversality of Representation in p-rings with Bounded Inversion
  • 8. Reduced $f$-Rings
  • 9. Strictly Representable Rings
  • 10. Quadratic Form Theory over Faithfully Quadratic Rings
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
Please select which format for which you are requesting permissions.