Finitary Prelinear and Linear Orthosets
| Autoři | |
|---|---|
| Rok publikování | 2023 |
| Druh | Článek v odborném periodiku |
| Časopis / Zdroj | International Journal of Theoretical Physics |
| Fakulta / Pracoviště MU | |
| Citace | |
| www | https://doi.org/10.1007/s10773-023-05356-2 |
| Doi | http://dx.doi.org/10.1007/s10773-023-05356-2 |
| Klíčová slova | Orthoset; Prelinear orthoset; Linear orthoset; Finite rank; Orthomodular lattice; Modular lattice; Covering property |
| Popis | 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. |
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