On the direct irreducibility of certain orthomodular lattices (Q1203439)
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scientific article; zbMATH DE number 118324
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the direct irreducibility of certain orthomodular lattices |
scientific article; zbMATH DE number 118324 |
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On the direct irreducibility of certain orthomodular lattices (English)
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8 February 1993
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Let \(F(L)\) be the ideal of all finite elements of an \(AC\)-lattice \(L\). The author notices that if \(L\) is a directly irreducible complete orthomodular \(AC\)-lattice of countably infinite length, \(F(L)\) is the only nontrivial standard ideal in the sense of \textit{G. Grätzer} and \textit{E. T. Schmidt} [Acta Math. Acad. Sci. Hung. 12, 17-86 (1961; Zbl 0115.019)]. This fact is applicable to test direct irreducibility for a given, complete orthomodular \(AC\)-lattice \(L\) of countably infinite length.
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orthomodular lattice
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\(AC\)-lattice
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standard ideal
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direct irreducibility
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