Noetherian and Artinian lattices (Q436521)
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scientific article; zbMATH DE number 6059357
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Noetherian and Artinian lattices |
scientific article; zbMATH DE number 6059357 |
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Noetherian and Artinian lattices (English)
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23 July 2012
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Summary: It is proved that if \(L\) is a complete modular lattice which is compactly generated, then \(\text{Rad}(L)/0\) is Artinian if and only if for every small element \(a\) of \(L\) the sublattice \(a/0\) is Artinian if and only if \(L\) satisfies DCC on small elements.
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Artinian lattice
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Noetherian lattice
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compactly generated lattice
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complete modular lattice
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