Some properties of congruence relations on orthomodular lattices (Q2773032)
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scientific article; zbMATH DE number 1709160
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some properties of congruence relations on orthomodular lattices |
scientific article; zbMATH DE number 1709160 |
Statements
24 March 2002
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orthomodular lattice
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congruence relation
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\(p\)-ideal
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congruence class
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congruence regular
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congruence uniform
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arithmetical
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Some properties of congruence relations on orthomodular lattices (English)
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Briefly speaking, an orthomodular lattice (OML) is a Boolean algebra where the distributive law is substituted by the weaker orthomodular law \(x\vee y=x\vee((x\vee y)\wedge x')\). The paper under review deals with OMLs. The structure of the lattice of \(p\)-ideals (which are in a bijective correspondence to congruence relations) as well as the structure of congruence classes is investigated. From these results the well-known fact that OMLs are congruence regular, congruence uniform and arithmetical is derived.
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