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Author:   Steven Givant ,  Paul Halmos
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2nd Revised edition
Dimensions:   Width: 15.50cm , Height: 3.10cm , Length: 23.50cm
Weight:   1.122kg
ISBN:  

9780387402932

ISBN 10:   0387402934
Pages:   574
Publication Date:   02 December 2008
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
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Table of Contents

Boolean Rings.- Boolean Algebras.- Boolean Algebras Versus Rings.- The Principle of Duality.- Fields of Sets.- Elementary Relations.- Order.- Infinite Operations.- Topology.- Regular Open Sets.- Subalgebras.- Homomorphisms.- Extensions of Homomorphisms.- Atoms.- Finite Boolean Algebras.- Atomless Boolean Algebras.- Congruences and Quotients.- Ideals and Filters.- Lattices of Ideals.- Maximal Ideals.- Homomorphism and Isomorphism Theorems.- The Representation Theorem.- Canonical Extensions.- Complete Homomorphisms and Complete Ideals.- Completions.- Products of Algebras.- Isomorphisms of Factors.- Free Algebras.- Boolean s-algebras.- The Countable Chain Condition.- Measure Algebras.- Boolean Spaces.- Continuous Functions.- Boolean Algebras and Boolean Spaces.- Duality for Ideals.- Duality for Homomorphisms.- Duality for Subalgebras.- Duality for Completeness.- Boolean s-spaces.- The Representation of s-algebras.- Boolean Measure Spaces.- Incomplete Algebras.- Duality for Products.- Sums of Algebras.- Isomorphisms of Countable Factors.

Reviews

From the reviews: Introduction to Boolean Algebras ! is intended for advanced undergraduates. Givant (Mills College) and Halmos ! using clear and precise prose, build the abstract theory of Boolean rings and algebras from scratch. ! the necessary topological material is developed within the book and an appendix on set theory is included. ! Includes an extensive bibliography and more than 800 exercises at all levels of difficulty. Summing Up: Highly recommended. Upper-division undergraduates, graduate students, researchers, and faculty. (S. J. Colley, Choice, Vol. 46 (10), June, 2009) The authors have written a book for advanced undergraduates and beginning graduate students. ! The authors start with the definition of Boolean rings and Boolean algebras, give examples and basic facts and compare both notions. ! There are a large number of exercises of varying level of difficulty. Hints for the solutions of the harder problems are given in an appendix. A detailed solutions manual for all exercises is available for instructors. The book can serve as a basis for a variety of courses. (Martin Weese, Zentralblatt MATH, Vol. 1168, 2009)

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