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@article{2358572,
author = {Emir, Kadir and Paseka, Jan and Vetterlein, Thomas},
article_number = {6},
doi = {http://dx.doi.org/10.1007/s10773-023-05356-2},
keywords = {Orthoset; Prelinear orthoset; Linear orthoset; Finite rank; Orthomodular lattice; Modular lattice; Covering property},
language = {eng},
issn = {0020-7748},
journal = {International Journal of Theoretical Physics},
title = {Finitary Prelinear and Linear Orthosets},
url = {https://doi.org/10.1007/s10773-023-05356-2},
volume = {62},
year = {2023}
}
TY - JOUR
ID - 2358572
AU - Emir, Kadir - Paseka, Jan - Vetterlein, Thomas
PY - 2023
TI - Finitary Prelinear and Linear Orthosets
JF - International Journal of Theoretical Physics
VL - 62
IS - 6
SP - 1-17
EP - 1-17
PB - Springer
SN - 00207748
KW - Orthoset
KW - Prelinear orthoset
KW - Linear orthoset
KW - Finite rank
KW - Orthomodular lattice
KW - Modular lattice
KW - Covering property
UR - https://doi.org/10.1007/s10773-023-05356-2
N2 - An orthoset is a set equipped with a symmetric and irreflexive binary relation. A linear orthoset is an orthoset such that for any two distinct elements e, f there is a third element g such that exactly one of f and g is orthogonal to e and the pairs e, f and e, g have the same orthogonal complement. Linear orthosets naturally arise from anisotropic Hermitian spaces. We moreover define an orthoset to be prelinear by assuming the above-mentioned property for non-orthogonal pairs e, f only. In this paper, we establish some structural properties of prelinear and linear orthosets under the assumption of finiteness or finite rank.
ER -
EMIR, Kadir, Jan PASEKA a Thomas VETTERLEIN. Finitary Prelinear and Linear Orthosets. \textit{International Journal of Theoretical Physics}. Springer, 2023, roč.~62, č.~6, s.~1-17. ISSN~0020-7748. Dostupné z: https://dx.doi.org/10.1007/s10773-023-05356-2.
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