On semicontinuous lattices and their distributive reflections (Q271689)
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scientific article; zbMATH DE number 6566261
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On semicontinuous lattices and their distributive reflections |
scientific article; zbMATH DE number 6566261 |
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On semicontinuous lattices and their distributive reflections (English)
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7 April 2016
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In this paper, a characterization of a distributive reflection is described. The main results the authors present are that for a complete lattice \(L\) the distributive reflection \(L_d\) is isomorphic to the lattice of all radicals determined by principal ideals of \(L\) in the set-inclusion, and that if a complete lattice \(L\) is semicontinuous and every semiprime element \(x\) of \(L\) is the largest in \(d(x)\) then \(L_d\) is a continuous lattice.
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continuous lattice
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semicontinuous
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distributive reflection
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radical
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semiprime ideal
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Scott continuous
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