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Orthomodular Lattices Which can be Covered by Finitely Many Blocks

Published online by Cambridge University Press:  20 November 2018

Günter Bruns  and
Richard Greechie
Günter Bruns
Affiliation:
McMaster University, Hamilton, Ontario
Richard Greechie
Affiliation:
Kansas State University, Manhattan, Kansas
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In our paper [3] we considered four nniteness conditions for an orthomodular lattice (abbreviated: OML) L and conjectured their equivalence. The only question left open in that paper was whether an OML L which can be covered by finitely many blocks (maximal Boolean subalgebras) has only finitely many blocks. In this paper we give an affirmative answer to this question, in fact, we prove the slightly stronger result:

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 34 , Issue 3 , 01 June 1982 , pp. 696 - 699
Copyright
Copyright © Canadian Mathematical Society 1982

References

1. Brouwer, A. E., An inequality for binary vector spaces (manuscript).Google Scholar
2. Bruns, G., Covering a Boolean algebra by subalgebras, Mathematisches Forschungsinstitut Oberwolfach, Tagungsbericht 23 (1980).Google Scholar
3. Bruns, G. and Greechie, R., Some finiteness conditions for orthomodular lattices, Can. J. Math. 34 (1982), 535–549.Google Scholar
4. Greechie, R., On generating distributive sublattices of orthomodular lattices, Proc. AMS 67 (1977), 17–22.Google Scholar
5. An addendum to On generating distributive sublattices of orthomodular lattices, Proc. AMS 76 (1979), 216–218.Google Scholar