Finitary Prelinear and Linear Orthosets
| Authors | |
|---|---|
| Year of publication | 2023 |
| Type | Article in Periodical |
| Magazine / Source | International Journal of Theoretical Physics |
| MU Faculty or unit | |
| Citation | |
| Web | https://doi.org/10.1007/s10773-023-05356-2 |
| 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 |
| Description | 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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