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A Finitely Generated Modular Ortholattice

Published online by Cambridge University Press:  20 November 2018

Christian Herrmann*
Affiliation:
Fachbereich Mathematik, Technische Hochschule D61 Darmstadt, W. Germany
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By an ortholattice we mean a lattice with 0 and 1 and a complementation operation which is an involutorial antiautomorphism. The free modular ortholattice on two generators has 96 elements—cf. J. Kotas [8].

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1981

References

1. Amemiya, I. and Halperin, I., Completed modular lattices, Canad. J. Math. 11 (1959), 481-520.Google Scholar
2. Birkoff, G., Lattice Theory, Providence 1967.Google Scholar
3. Day, A., Herrman, C., and Wille, R., On modular lattices with four generators, Algebra Universalis. 2 (1972), 317-323.Google Scholar
4. Gel'fand, I. M. and Ponomarev, V. A., Problems of linear algebra and classification of quadruples of subspaces in a finite dimensional vector space, Coll. Math. J. Bolyai, 5, Hilbert Space Operators, Tihany 1970; -Nagy, B.Sz. (ed), North-Holland, Amsterdam, 1972, 163-237.Google Scholar
5. Herrmann, C., On the equational theory of submodule lattices, Proc. Univ. of Huston Lattice Theory Conf. 1973, 105-108.Google Scholar
6. Kaplansky, I., Any orthocomplemented complete modular lattice is a continuous geometry, Ann. of Math.. 61 (1955), 524-541.Google Scholar
7. Kalmbach, G., Orthomodular lattices, Lecture Notes, to appear.Google Scholar
8. Kotas, J., An axiom system for the modular logic. Studia logica XXI (1967), 17-38.Google Scholar
9. Mal'cev, A. I., The metamathematics of algebraic systems, Amsterdam 1971.Google Scholar
10. Poguntke, W., Zerlegung von S-Verbânden, Math. Z. 142 (1975), 47-65.Google Scholar