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Lectures on Boolean algebras

Author: Paul R Halmos
Publisher: Mineola, New York : Dover Publications, Inc., 2018.
Series: Dover books in science and mathematics.; Dover books on mathematics.
Edition/Format:   eBook : Document : English : Dover editionView all editions and formats
Summary:
This presentation on the basics of Boolean algebra has ranked among the fundamental books on this important subject in mathematics and computing science since its initial publication in 1963. Concise and informal as well as systematic, the text draws upon lectures delivered by Professor Halmos at the University of Chicago to cover many topics in brief individual chapters. The approach is suitable for advanced  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Halmos, Paul R. (Paul Richard), 1916-2006.
Lectures on Boolean algebras.
Mineola, New York : Dover Publications, Inc., 2018
(DLC) 2018010158
(OCoLC)1029062425
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Paul R Halmos
ISBN: 9780486834573 0486834573
OCLC Number: 1053817545
Notes: Originally published: London, England ; Princeton, N.J. : Van Nostrand, 1963.
Description: 1 online resource (147 pages) : illustrations.
Contents: Boolean rings --
Boolean algebras --
Fields of sets --
Regular open sets --
Elementary relations --
Order --
Infinite operations --
Subalgebras --
Homomorphisms --
Free algebras --
Ideals and filters --
The homomorphism theorem --
Boolean o-algebras --
The countable chain condition --
Measure algebras --
Atoms --
Boolean spaces --The representation theorem --
Duality for ideals --
Duality for homomorphisms --
Completion --
Boolean o-spaces --
The representation of o-algebras --
Boolean measure spaces --
Incomplete algebras --
Products of algebras --
Sums of algebras --
Isomorphisms of factors --
Isomorphisms of countable factors --
Retracts --
Projective algebras --
Injective algebras.
Series Title: Dover books in science and mathematics.; Dover books on mathematics.
Other Titles: Boolean algebras
Responsibility: Paul R. Halmos.

Abstract:

This presentation on the basics of Boolean algebra has ranked among the fundamental books on this important subject in mathematics and computing science since its initial publication in 1963. Concise and informal as well as systematic, the text draws upon lectures delivered by Professor Halmos at the University of Chicago to cover many topics in brief individual chapters. The approach is suitable for advanced undergraduates and graduate students in mathematics. Starting with Boolean rings and algebras, the treatment examines fields of sets, regular open sets, elementary relations, infinite operations, subalgebras, homomorphisms, free algebras, ideals and filters, and the homomorphism theorem. Additional topics include measure algebras, Boolean spaces, the representation theorem, duality for ideals and for homomorphisms, Boolean measure spaces, isomorphisms of factors, projective and injective algebras, and many other subjects. Several chapters conclude with stimulating exercises; the solutions are not included.

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