Geodesic
Orthomodular lattices that are horizontal sums of Boolean algebras
Commentationes Mathematicae Universitatis Carolinae, Tome 61 (2020) no. 1, pp. 11-20.

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The paper deals with orthomodular lattices which are so-called horizontal sums of Boolean algebras. It is elementary that every such orthomodular lattice is simple and its blocks are just these Boolean algebras. Hence, the commutativity relation plays a key role and enables us to classify these orthomodular lattices. Moreover, this relation is closely related to the binary commutator which is a term function. Using the class $\mathcal H$ of horizontal sums of Boolean algebras, we establish an identity which is satisfied in the variety generated by $\mathcal H$ but not in the variety of all orthomodular lattices. The concept of ternary discriminator can be generalized for the class $\mathcal H$ in a modified version. Finally, we present several results on varieties generated by finite subsets of finite members of $\mathcal H$.
DOI : 10.14712/1213-7243.2020.003
Classification : 06C15, 06C20, 06E75
Keywords: orthomodular lattice; horizontal sum; commuting elements; Boolean algebra 
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Chajda, Ivan; Länger, Helmut. Orthomodular lattices that are  horizontal sums of Boolean algebras. Commentationes Mathematicae Universitatis Carolinae, Tome 61 (2020) no. 1, pp. 11-20. doi : 10.14712/1213-7243.2020.003. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2020.003/

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