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Projective Orthomodular Lattices

Published online by Cambridge University Press:  20 November 2018

Gunter Bruns  and
Michael Roddy
Gunter Bruns
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L8S 4K1
Michael Roddy
Affiliation:
Department of Mathematics and Computer Science Brandon University Brandon, Manitoba R7A 6A9
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Abstract

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We introduce sectional projectivity, which appears to be the correct notion of projectivity when working with orthomodularlattices. We prove some positive results for varieties of OMLs satisfying various finiteness conditions, namely that every finite OML in such a variety is sectionally projective. In contrast, we prove that the eight element modular ortholattice, MO 3, is not projective in the variety of modular ortholattices.

Keywords

06C15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 2 , 01 June 1994 , pp. 145 - 153
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Beran, L., Orthomodular lattices, D. Reidel, Dordrecht, 1985.Google Scholar
2. Bruns, G., Greechie, R., Harding, J. and Roddy, M., Completions of orthomodular lattices, Order 7(1990), 67–76.Google Scholar
3. Bruns, G. and Kalmbach, G., Some remarks on free orthomodular lattices, Proc. lattice theory conference (ed. J. Schmidt), Houston, (1973), 397–408.Google Scholar
4. Bruns, G. and Roddy, M., A finitely generated modular ortholattice, Canad. Math. Bull. 35(1992), 29–33.Google Scholar
5. Day, A., Herrmann, C. and Wille, R., On modular lattices with four generators, Algebra Universalis 2(1972), 317–323.Google Scholar
6. Halmos, P., Injective and projective boolean algebras, Proc. Sympos. Pure Math. II, (1961), 114–122.Google Scholar
7. Jônsson, B., Algebras whose congruence lattices are distributive, Math. Scand. 21(1967), 110–121.Google Scholar
8. Kalmbach, G., Orthomodular Lattices, Academic Press, London, 1983.Google Scholar