A characterization of modularity and orthomodularity (Q1061154)
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scientific article; zbMATH DE number 3908491
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A characterization of modularity and orthomodularity |
scientific article; zbMATH DE number 3908491 |
Statements
A characterization of modularity and orthomodularity (English)
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1986
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The following theorem is proved: A lattice is modular iff it satisfies the distributivity laws for all triples of elements at least two of which are comparable. Modularity of a lattice is even equivalent to each single one of these distributivity conditions that is not trivially satisfied. An ortholattice is orthomodular iff it satisfies the distributivity laws for all triples of elements at least two of which are comparable and at least two of which are orthogonal. For ortholattices orthomodularity is even equivalent to each single one of these distributivity conditions that is not trivially satisfied.
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distributivity conditions
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ortholattice
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orthomodularity
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