Absorption (mathematics)

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:

$x\wedge (x\vee y)=x;~x\vee (x\wedge y)=x.\,$

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

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