**Memoirs of the American Mathematical Society**

2015;
129 pp;
Softcover

MSC: Primary 11; 12; 03; 06; 46; 54;

Print ISBN: 978-1-4704-1468-9

Product Code: MEMO/238/1128

List Price: $81.00

Individual Member Price: $48.60

**Electronic ISBN: 978-1-4704-2629-3
Product Code: MEMO/238/1128.E**

List Price: $81.00

Individual Member Price: $48.60

# Faithfully Quadratic Rings

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*M. Dickmann; F. Miraglia*

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

# Table of Contents

## Faithfully Quadratic Rings

- Cover Cover11 free
- Title page i2 free
- Preface vii8 free
- Chapter 1. Basic Concepts 114 free
- Chapter 2. Rings and Special Groups 922
- Chapter 3. The Notion of T-Faithfully Quadratic Ring. Some Basic Consequences 2740
- Chapter 4. Idempotents, Products and T-isometry 4154
- Chapter 5. First-Order Axioms for Quadratic Faithfulness 5366
- Chapter 6. Rings with Many Units 6174
- Chapter 7. Transversality of Representation in p-rings with Bounded Inversion 6982
- Chapter 8. Reduced 𝑓-Rings 7588
- Chapter 9. Strictly Representable Rings 101114
- Chapter 10. Quadratic Form Theory over Faithfully Quadratic Rings 111124
- Bibliography 121134
- Index of Symbols 125138 free
- Subject Index 127140
- Back Cover Back Cover1148