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complementedlattice

complemented lattice

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Definitions of complemented lattice in various dictionaries:

COMPLEMENTED LATTICE - In the mathematical discipline of order theory, a complemented lattice is a bounded lattice (with least element 0 and greatest element 1), in which e...

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Complemented lattice might refer to
In the mathematical discipline of order theory, a Complemented lattice is a bounded lattice (with least element 0 and greatest element 1), in which every element a has a complement, i.e. an element b satisfying a ∨ b = 1 and a ∧ b = 0. * Complements need not be unique. * A relatively complemented lattice is a lattice such that every interval [c, d], viewed as a bounded lattice in its own right, is a complemented lattice. * An orthocomplementation on a complemented lattice is an involution which is order-reversing and maps each element to a complement. An orthocomplemented lattice satisfying a weak form of the modular law is called an orthomodular lattice. * In distributive lattices, complements are unique. Every complemented distributive lattice has a unique orthocomplementation and is in fact a Boolean algebra.*

Complemented lattice might refer to

In the mathematical discipline of order theory, a Complemented lattice is a bounded lattice (with least element 0 and greatest element 1), in which every element a has a complement, i.e. an element b satisfying a ∨ b = 1 and a ∧ b = 0.
* Complements need not be unique.
* A relatively complemented lattice is a lattice such that every interval [c, d], viewed as a bounded lattice in its own right, is a complemented lattice.
* An orthocomplementation on a complemented lattice is an involution which is order-reversing and maps each element to a complement. An orthocomplemented lattice satisfying a weak form of the modular law is called an orthomodular lattice.
* In distributive lattices, complements are unique. Every complemented distributive lattice has a unique orthocomplementation and is in fact a Boolean algebra.*

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