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Autometrized Boolean Algebras II

The Group of Motions of B

Published online by Cambridge University Press:  20 November 2018

David Ellis
David Ellis*
Affiliation:
University of Missouri
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The writer [1] has previously examined the fundamental concepts of distance geometry in a Boolean algebra, B, with distance defined by . Any technical terms from distance geometry which are not defined in this paper may be found in [1]. A Boolean algebra bearing the given distance function is called an autometrized Boolean algebra. It is clear that the set of motions B (congruences of B with itself) form a group under substitution. This group we denote by M(B).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 3 , 1951 , pp. 145 - 147
Copyright
Copyright © Canadian Mathematical Society 1951

References

[1] Ellis, David, Autometrized Boolean algebras J, Can. J. Math., vol. 3 (1951), 87–93.Google Scholar
[2] Stone, M. H., Subsumption of Boolean algebras under the theory of rings, Proc. Nat. Acad. Sci., vol. 20 (1934), 197–202.Google Scholar