The Structure of Relation Algebras Generated by Relativizations

The Structure of Relation Algebras Generated by Relativizations

by Givant
     
 

ISBN-10: 0821851772

ISBN-13: 9780821851777

Pub. Date: 02/08/1994

Publisher: American Mathematical Society

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

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Overview

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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Product Details

ISBN-13:
9780821851777
Publisher:
American Mathematical Society
Publication date:
02/08/1994
Series:
Contemporary Mathematics Series, #156
Pages:
134
Product dimensions:
7.09(w) x 10.24(h) x (d)

Related Subjects

Table of Contents

Introduction
Ch. 1Basic Definitions and Laws1
Ch. 2Algebraic Notions15
Ch. 3The Characteristic of an Equivalence Element31
Ch. 4The Arithmetic of Rectangles51
Ch. 5Structure Theorems67
Ch. 6Existence, Uniqueness, and Representation Theorems89
Ch. 7Relation Algebras Generated by Equivalence Elements109
Bibliography127
Index of Symbols129
Index of Names and Subjects131

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