Chajda, Ivan, and Länger, Helmut. "Orthomodular lattices that are horizontal sums of Boolean algebras." Commentationes Mathematicae Universitatis Carolinae 61.1 (2020): 11-20. <http://eudml.org/doc/297325>.
@article{Chajda2020,
abstract = {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 $\mathcal \{H\}$.},
author = {Chajda, Ivan, Länger, Helmut},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {orthomodular lattice; horizontal sum; commuting elements; Boolean algebra},
language = {eng},
number = {1},
pages = {11-20},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Orthomodular lattices that are horizontal sums of Boolean algebras},
url = {http://eudml.org/doc/297325},
volume = {61},
year = {2020},
}
TY - JOUR
AU - Chajda, Ivan
AU - Länger, Helmut
TI - Orthomodular lattices that are horizontal sums of Boolean algebras
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2020
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 61
IS - 1
SP - 11
EP - 20
AB - 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 $\mathcal {H}$.
LA - eng
KW - orthomodular lattice; horizontal sum; commuting elements; Boolean algebra
UR - http://eudml.org/doc/297325
ER -
