A note on commutative multiplicative semilattices (Q1121296)
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scientific article; zbMATH DE number 4103140
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on commutative multiplicative semilattices |
scientific article; zbMATH DE number 4103140 |
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A note on commutative multiplicative semilattices (English)
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1989
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The author establishes some equivalent conditions for the lattice of filters of a bounded commutative multiplicative semilattice to be an infinite meet distributive lattice. Using these, the author proves the following. Theorem. A bounded commutative multiplicative semilattice S is a finite Boolean algebra if and only if S satisfies the following three conditions: (i) S is semiprime; (ii) S is semicomplimented; (iii) every completely meet irreducible filter is completely meet prime.
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lattice of filters of a bounded commutative multiplicative semilattice
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infinite meet distributive lattice
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finite Boolean algebra
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semiprime
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semicomplimented
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irreducible
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