The Structure of Relation Algebras Generated by Relativizations

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Brand new. We distribute directly for the publisher. The foundation for an algebraic theory of binary relations was laid by De Morgan, Peirce, and Schrder 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. Read more Show Less

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The foundation for an algebraic theory of binary relations was laid by De Morgan, Peirce, and Schroder 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.

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An accessible analysis of 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). Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

Table of Contents

Introduction
Ch. 1 Basic Definitions and Laws 1
Ch. 2 Algebraic Notions 15
Ch. 3 The Characteristic of an Equivalence Element 31
Ch. 4 The Arithmetic of Rectangles 51
Ch. 5 Structure Theorems 67
Ch. 6 Existence, Uniqueness, and Representation Theorems 89
Ch. 7 Relation Algebras Generated by Equivalence Elements 109
Bibliography 127
Index of Symbols 129
Index of Names and Subjects 131
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