**Contemporary Mathematics**

Volume: 156;
1994;
134 pp;
Softcover

MSC: Primary 03;
Secondary 08

**Print ISBN: 978-0-8218-5177-7
Product Code: CONM/156**

List Price: $33.00

AMS Member Price: $26.40

MAA Member Price: $29.70

**Electronic ISBN: 978-0-8218-7747-0
Product Code: CONM/156.E**

List Price: $31.00

AMS Member Price: $24.80

MAA Member Price: $27.90

# The Structure of Relation Algebras Generated by Relativizations

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*Steven R. Givant*

The foundation for an algebraic theory of binary relations was laid by De Morgan, Peirce, and Schröder during the second half of the nineteenth century. Modern development of the subject as a theory of abstract algebras, called “relation algebras”, was undertaken by Tarski and his students. This book aims to analyze the structure of relation algebras that are generated by relativized subalgebras. As examples of their potential for applications, the main results are used to establish representation theorems for classes of relation algebras and to prove existence and uniqueness theorems for simple closures (i.e., for minimal simple algebras containing a given family of relation algebras as relativized subalgebras). This book is well written and accessible to those who are not specialists in this area. In particular, it contains two introductory chapters on the arithmetic and the algebraic theory of relation algebras. This book is suitable for use in graduate courses on algebras of binary relations or algebraic logic.

#### Readership

Graduate students and mathematicians.

#### Reviews & Endorsements

The monograph is highly readable, well illustrated …

-- Zentralblatt MATH

# Table of Contents

## The Structure of Relation Algebras Generated by Relativizations

- Contents vii8 free
- Introduction ix10 free
- Chapter 1. Basic Definitions and Laws 118 free
- Chapter 2. Algebraic Notions 1532
- Chapter 3. The Characteristic of an Equivalence Element 3148
- Chapter 4. The Arithmetic of Rectangles 5168
- Chapter 5. Structure Theorems 6784
- Chapter 6. Existence, Uniqueness, and Representation Theorems 89106
- Chapter 7. Relation Algebras Generated by Equivalence Elements 109126
- Bibliography 127144
- Index of Symbols 129146 free
- Index of Names and Subjects 131148 free