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A Self-Dual Equational Basis for Boolean Algebras

Published online by Cambridge University Press:  20 November 2018

R. Padmanabhan
R. Padmanabhan*
Affiliation:
University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2
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Abstract

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The principle of duality for Boolean algebra states that if an identity ƒ = g is valid in every Boolean algebra and if we transform ƒ = g into a new identity by interchanging (i) the two lattice operations and (ii) the two lattice bound elements 0 and 1, then the resulting identity ƒ = g is also valid in every Boolean algebra. Also, the equational theory of Boolean algebras is finitely based. Believing in the cosmic order of mathematics, it is only natural to ask whether the equational theory of Boolean algebras can be generated by a finite irredundant set of identities which is already closed for the duality mapping. Here we provide one such equational basis.

Keywords

03G0506E99Boolean algebrasduality principleminimal self-dual equational basistypes of algebras
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 1 , 01 March 1983 , pp. 9 - 12
Copyright
Copyright © Canadian Mathematical Society 1983

References

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