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Stone algebra
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In mathematics, a Stone algebra or Stone lattice is a pseudocomplemented distributive lattice L in which any of the following equivalent statements hold for all [1]
- ;
- ;
- .
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They were introduced by Grätzer & Schmidt (1957) and named after Marshall Harvey Stone.
The set is called the skeleton of L. Then L is a Stone algebra if and only if its skeleton S(L) is a sublattice of L.[1]
Boolean algebras are Stone algebras, and Stone algebras are Ockham algebras.
Examples:
- The open-set lattice of an extremally disconnected space is a Stone algebra.
- The lattice of positive divisors of a given positive integer is a Stone lattice.
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