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- W4243119448 abstract "In this paper we continue the study of equationally defined classes of orthomodular lattices started in [ 1 ]. The only atom in the lattice of varieties of orthomodular lattices is the variety of all Boolean algebras. Every nontrivial variety contains it. It follows from B. Jónsson [ 4 , Corollary 3.2] that the variety [MO2] generated by the orthomodular lattice MO2 of Figure 1 covers the variety of all Boolean algebras. I t was first shown by R. J. Greechie (oral communication) and is not difficult to see that every variety not consisting of Boolean algebras only contains [MO2]. Again it follows from the result of Jónsson's mentioned above that the varieties generated by one of the orthomodular lattices of Figures 2 to 5 cover [MO2]. The Figures 4 and 5 are to be understood in such a way that the orthocomplement of every element is on the vertical line through this element." @default.
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- W4243119448 date "1972-04-01" @default.
- W4243119448 modified "2023-10-01" @default.
- W4243119448 title "Varieties of Orthomodular Lattices. II" @default.
- W4243119448 doi "https://doi.org/10.4153/cjm-1972-027-4" @default.
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