# Absorption (mathematics)

From Citizendium

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:

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

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