On varieties of modular ortholattices that are generated by their finite-dimensional members.
A modular ortholattice is an algebra \((L,\vee,\wedge,',0,1)\) of type \((2,2,1,0,0)\) such that \((L,\vee,\wedge,0,1)\) is a bounded modular lattice and the identities \(x\vee x'=1\), \(x\wedge x'=0\), \((x')'=x\), \((x\vee y)'=x'\wedge y'\) and \((x\wedge y)'=x'\vee y'\) hold. Let \(\mathcal L\) be a modular ortholattice and \(\mathcal V\) a variety of modular ortholattices. The dimension of \(\mathcal L\) is the cardinality of a maximal chain in \(\mathcal L\) minus one. The fact that \(\mathcal L\) belongs to the variety generated by the finite-dimensional members of \(\mathcal V\) is characterized in two different ways.
finite-dimensional modular ortholattices
scientific article; zbMATH DE number 6384896