Contemporary Mathematics 1994; 134 pp; softcover Volume: 156 ISBN10: 0821851772 ISBN13: 9780821851777 List Price: US$29 Member Price: US$23.20 Order Code: CONM/156
 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
