Abstract
We prove that the following three conditions on a modular ortholattice L with respect to a given variety of modular ortholattices, \({\mathcal{V}}\), are equivalent: L is in the variety of modular ortholattices generated by the finite-dimensional members of \({\mathcal{V}}\); L can be embedded in an atomisticmember of \({\mathcal{V}}\); L has an orthogeometric representation in an anisotropic orthogeometry \({{(Q,\bot), \,\,{\rm where}\,\, [0, u] \in \mathcal{V} \,\,{\rm for\,\, all}\,\, u \in L_{\rm fin}(Q)}}\).
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Herrmann, C., Roddy, M.S. On varieties of modular ortholattices that are generated by their finite-dimensional members. Algebra Univers. 72, 349–357 (2014). https://doi.org/10.1007/s00012-014-0305-0
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DOI: https://doi.org/10.1007/s00012-014-0305-0