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The Structure of Relation Algebras Generated by Relativizations
Steven R. Givant, Mills College, Oakland, CA
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Contemporary Mathematics
1994; 134 pp; softcover
Volume: 156
ISBN-10: 0-8218-5177-2
ISBN-13: 978-0-8218-5177-7
List Price: US$29
Member Price: US$23.20
Order Code: CONM/156
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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

"The monograph is highly readable, well illustrated ..."

-- Zentralblatt MATH

Table of Contents

  • Basic definitions and laws
  • Algebraic notions
  • The characteristic of an equivalence element
  • The arithmetic of rectangles
  • Structure theorems
  • Existence, uniqueness, and representation theorems
  • Relation algebras generated by equivalence elements
  • Bibliography
  • Index of symbols
  • Index of names and subjects
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