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The free orthomodular word problem is solvable

Published online by Cambridge University Press:  17 April 2009

Gudrun Kalmbach
Gudrun Kalmbach
Affiliation:
Abt. Math. III, O.E., University Ulm, D-7900 ULM, West Germany.
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Abstract

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It is shown that the free orthomodular word problem is solvable. Since the free orthomodular lattice L0 on countable many generators has, as a partial subalgebra, every finite partial orthomodular lattice P, which is contained in some orthomodular lattice as a partial subalgebra, it is sufficient to prove Evans embedding property for these P only. The construction of the finite orthomodular lattice containing P as a partial subalgebra has and can be done outside of L0. It uses the coatom extension for ortholattices.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 34 , Issue 2 , October 1986 , pp. 219 - 223
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Evans, T., “Embeddability and the word problem,” J. London Math. Soc. 28 (1953), 76–80.CrossRefGoogle Scholar
[2]Kalmbach, G., Orthomodular lattices. (Academic Press, London, 1983).Google Scholar