Hostname: page-component-7479d7b7d-fwgfc Total loading time: 0 Render date: 2024-07-12T19:23:02.686Z Has data issue: false hasContentIssue false
  • English
  • Français

QUANTUM LOGIC ASSOCIATED TO FINITE DIMENSIONAL INTERVALS OF MODULAR ORTHOLATTICES

Published online by Cambridge University Press:  29 June 2016

R. GIUNTINI ,
H. FREYTES  and
G. SERGIOLI
R. GIUNTINI
Affiliation:
UNIVERSITÁ DI CAGLIARI VIA IS MIRRIONIS 1, 09123 CAGLIARI, ITALIAE-mail:giuntini@unica.it
H. FREYTES
Affiliation:
DEPARTAMENTO DE MATEMÁTICA UNR-CONICET AV. PELLEGRINI 250 CP 2000, ROSARIO, ARGENTINAE-mail:hfreytes@gmail.com
G. SERGIOLI
Affiliation:
UNIVERSITÁ DI CAGLIARI VIA IS MIRRIONIS 1, 09123 CAGLIARI, ITALIAE-mail:giuseppe.sergioli@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

In this work we study an abstract formulation of a problem posed by J.M. Dunn, T.J. Hagge et al. about the inclusion of varieties generated by the modular ortholattice of subspaces of ℂn. We shall prove that, this abstract formulation is equivalent to the direct irreducibility for atomic complete modular ortholattices.

Keywords

06Cxx06B20modular ortholatticesdimensiondirect irreducibility
Type
Articles
Information
The Journal of Symbolic Logic , Volume 81 , Issue 2 , June 2016 , pp. 629 - 640
Copyright
Copyright © The Association for Symbolic Logic 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Birkhoff, G. and von Neumann, J., The logic of quantum mechanics . Annals of Mathematics, vol. 37 (1936), pp. 823–843.Google Scholar
Burris, S., Sankappanavar, H. P., A Course in Universal Algebra, Graduate Text in Mathematics, vol. 78, Springer-Verlag, New York, Heidelberg, Berlin, 1981.Google Scholar
Catlin, D. E., Irreducibility conditions in orthomodular lattices . Journal of Natural Sciences and Mathematics, vol. 8 (1968), pp. 81–87.Google Scholar
Dunn, J. M., Hagge, T. J., Moss, L. S. and Wang, Z., Quantum logic as motived by quantum computing, this Journal, vol. 70 (2005), pp. 353–359.Google Scholar
Hagge, T. J., QL(ℂ n ) determines n, this Journal, vol. 72 (2007), pp. 1194–1196.Google Scholar
Kalmbach, G., Orthomodular Lattices, Academic Press, New York, 1983.Google Scholar
Maeda, F. and Maeda, S., Theory of Symmetric Lattices, Springer-Verlag, Berlin, 1970.Google Scholar