Absorption (Mathematics)

	Main Article	Discussion	Related Articles  [?]	Bibliography  [?]	External Links  [?]	Citable Version  [?]
	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:

${\displaystyle x\wedge (x\vee y)=x;x\vee (x\wedge y)=x.}$

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[edit]

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