On complements in lattices with covering properties (Q1185230)
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scientific article; zbMATH DE number 37904
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On complements in lattices with covering properties |
scientific article; zbMATH DE number 37904 |
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On complements in lattices with covering properties (English)
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28 June 1992
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An atomistic lattice which covering property is called an AC-lattice. A finite element means either 0 or an element which is a join of finitely many atoms. The author proves: Let \(L\) be a complete finite-modular AC- lattice and let \(b\) be a finite element of \(L\). Then \(b\) has a complement iff \(1_ +=0\), where \(1_ +\) denotes the meet of all lower covers of 1.
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complemented elements
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atomistic lattice
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covering property
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AC-lattice
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