Absorption (mathematics): Difference between revisions
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In [[algebra]], '''absorption''' is a property of [[binary operation]]s which reflects an underlying [[order (relation)|order relation]]. | In [[algebra]], '''absorption''' is a property of [[binary operation]]s which reflects an underlying [[order (relation)|order relation]]. | ||
Revision as of 14:16, 6 February 2009
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.