Orthomodular lattices that are horizontal sums of Boolean algebras

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F20%3A73603117" target="_blank" >RIV/61989592:15310/20:73603117 - isvavai.cz</a>
Result on the web
<a href="https://obd.upol.cz/id_publ/333183003" target="_blank" >https://obd.upol.cz/id_publ/333183003</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.14712/1213-7243.2020.003" target="_blank" >10.14712/1213-7243.2020.003</a>

Result language
angličtina
Original language name
Orthomodular lattices that are horizontal sums of Boolean algebras
Original language description
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 H of horizontal sums of Boolean algebras, we establish an identity which is satisfied in the variety generated by H but not in the variety of all orthomodular lattices. The concept of ternary discriminator can be generalized for the class H in a modified version. Finally, we present several results on varieties generated by finite subsets of finite members of H.
Czech name
—
Czech description
—

Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GF20-09869L" target="_blank" >GF20-09869L: The many facets of orthomodularity</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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