Finitely generated free modular ortholattices. I - Haviar, M; Konopka, P; Priestley, H; Wegener, C (1997)
A description is given of the n-generated free algebras in the variety of modular ortholattices generated by an ortholattice MO2 of height 2 with 4 atoms. In the subvariety lattice of orthomodular lattices, the variety V(MO2) is the unique cover of the variety of Boolean algebras, in which n-generated free algebras were described by G. Boole in 1854. It is shown that the n-generated free algebra in the variety V(MO2) is a product of the n -generated free Boolean algebra 22″ and Φ(n) copies of the generator MO2, and formula is presented for Φ(n). To achieve this result, algebraic methods of the theory of orthomodular lattices are combined with recently developed methods of natural duality theory for varieties of algebras.