Abstract
In a paper on the foundation of quantum mechanics, Kôdi Husimi(1) conjectured that a lattice with a negation is modular if the chain law holds for every sublattice closed with respect to relative negation. Although the theorem in this form does not hold, as we show by an example, we prove a theorem of a similar nature for relatively complemented lattices.
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References
K. Husimi, Studies on the foundations of quantum mechanics. Proc. of the Physico-Math. Soc. of Japan, 19 (1937), pp. 766–789.
G. Birkhoff and M. Ward, Bull, of the Amer. Math. Soc., abstract (45-1-78).
Garrett Birkhoff. On combination of suhalgebra, Proc. of the Cambridge Phil. Soc., 29 (1933), pp. 441–464.
See for example, Huntington, Trans. Amer. Math. Soc., 5 (1904), p. 288; Skolem, Videnskapsselskepets Skrifter (1919); Bergman, Monatshefte f. Math. u. Phys., 36 (1929).
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© 1990 Springer Science+Business Media New York
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Dilworth, R.P. (1990). On Complemented Lattices. In: Bogart, K.P., Freese, R., Kung, J.P.S. (eds) The Dilworth Theorems. Contemporary Mathematicians. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4899-3558-8_7
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DOI: https://doi.org/10.1007/978-1-4899-3558-8_7
Publisher Name: Birkhäuser, Boston, MA
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