Lectures on Boolean Algebras

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  • Format: Paperback
  • Copyright: 2018-09-12
  • Publisher: Dover Publications

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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.

Author Biography

Paul R. Halmos (1916–2006) was a prominent American mathematician who taught at the University of Chicago, the University of Michigan, and other schools and made significant contributions to several areas of mathematics, including mathematical logic, ergodic theory, functional analysis, and probability theory. His other Dover books are Algebraic Logic, Finite-Dimensional Vector Spaces, Introduction to Hilbert Space and the Theory of Spectral Multiplicity, Lectures on Ergodic Theory, and Naive Set Theory.

Table of Contents

1. Boolean rings
2. Boolean algebras
3. Fields of sets
4. Regular open sets
5. Elementary relations
6. Order
7. Infinite operations
8. Subalgebras
9. Homomorphisms
10. Free algebras
11. Ideals and filters
12. The homomorphism theorem
13. Boolean o-algebras
14. The countable chain condition
15. Measure algebras
16. Atoms
17. Boolean spaces
18. The representation theorem
19. Duality for ideals
20. Duality for homomorphisms
21. Completion
22. Boolean o-spaces
23. The representation of o-algebras
24. Boolean measure spaces
25. Incomplete algebras
26. Products of algebras
27. Sums of algebras
28. Isomorphisms of factors
29. Isomorphisms of countable factors
30. Retracts
31. Projective algebras
32. Injective algebras

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