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Homomorphisms

  • Paul R. Halmos
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

A Boolean homomorphism is a mapping f from a Boolean algebra B, say, to a Boolean algebra A,such that
$$ f(p \wedge q) = f(p) \wedge f(q), $$
(1)
$$ f(p \vee q) = f(p) \vee f(q), $$
(2)
$$ f(p') = (f(p))', $$
(3)
whenever p and q are in B. In a somewhat loose but brief and suggestive phrase, a homomorphism is a structure-preserving mapping between Boolean algebras. A convenient synonym for “homomorphism from B to A” is “A-valued homomorphism on B”. Such expressions will be used most frequently in case A = 2.

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Copyright information

© Springer-Verlag New York Inc. 1974

Authors and Affiliations

  • Paul R. Halmos
    • 1
  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA

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