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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]

  • ;
  • ;
  • .

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:

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See also

References

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