Absorption (mathematics)

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This editable Main Article is under development and subject to a disclaimer.

[edit intro]

In algebra, absorption is a property of binary operations which reflects an underlying order relation.

Sometimes called the "absorption law", it is one of the defining properties of a lattice:

x∧(x∨y)=x;x∨(x∧y)=x.

Examples include

* In set theory, intersection and union;
* In propositional logic, conjunction (logical and) and disjunction (logical or);
* In a distributive lattice, join and meet;
* In a linearly ordered set, minimum and maximum;
* In the integers, highest common factor and least common multiple;

## References[edit]

* A.G. Howson (1972). A handbook of terms used in algebra and analysis. Cambridge University Press, 76\. ISBN 0-521-09695-2.