Modularity and distributivity in the subideal lattice of a Lie algebra (Q1060272)
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scientific article; zbMATH DE number 3906684
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Modularity and distributivity in the subideal lattice of a Lie algebra |
scientific article; zbMATH DE number 3906684 |
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Modularity and distributivity in the subideal lattice of a Lie algebra (English)
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1985
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This article gives necessary and sufficient conditions for the subideal lattice of a finite-dimensional Lie algebra over a field of characteristic zero to be (1) modular and (2) distributive. A Lie algebra \(L\) for which the relation of being an ideal in \(L\) is transitive is called a \({\mathcal T}\)-Lie algebra. Equivalent conditions for the subideal lattice of such an algebra to be distributive are derived.
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modular lattice
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distributive lattice
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transitive Lie algebra
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subideal lattice
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finite-dimensional Lie algebra
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characteristic zero
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