1-distributive lattice with pm-property (Q2716723)
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scientific article; zbMATH DE number 1599364
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | 1-distributive lattice with pm-property |
scientific article; zbMATH DE number 1599364 |
Statements
1 November 2001
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1-distributive lattices
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pm-property
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Stone space
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normal topological space
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prime ideal
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maximal ideal
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1-distributive lattice with pm-property (English)
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A lattice is said to be 1-distributive if it possesses a top element and each maximal ideal in it is prime. It is proved that the Stone space of a 1-distributive lattice \(L\) is normal if and only if each prime ideal in \(L\) is contained in a unique maximal ideal.
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