Geometric exchange properties in lattices of finite length (Q799703)
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scientific article; zbMATH DE number 3873392
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Geometric exchange properties in lattices of finite length |
scientific article; zbMATH DE number 3873392 |
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Geometric exchange properties in lattices of finite length (English)
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1984
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A semimodular lattice is strong if every contraction map is onto on join irreducibles. The authors give three equivalent characterizations by exchange properties: a strengthening of MacLane's and that of Gaskill and Rival within all lattices of finite length, that of Kurosh-Ore within the semimodular ones. For the latter, excluding the minimal semimodular, but not dually semimodular lattice as an isometric sublattice is sufficient, too.
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semimodular lattice
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contraction map
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join irreducibles
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exchange properties
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lattices of finite length
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