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- Absorption_law abstract "In algebra, the absorption law or absorption identity is an identity linking a pair of binary operations.Two binary operations, ¤ and ⁂, are said to be connected by the absorption law if:a ¤ (a ⁂ b) = a ⁂ (a ¤ b) = a.A set equipped with two commutative, associative and idempotent binary operations ("join") and ("meet") that are connected by the absorption law is called a lattice.Examples of lattices include Boolean algebras, the set of sets with union and intersection operators, Heyting algebras, and ordered sets with min and max operations.In classical logic, and in particular Boolean algebra, the operations OR and AND, which are also denoted by and , satisfy the lattice axioms, including the absorption law. The same is true for intuitionistic logic.The absorption law does not hold in many other algebraic structures, such as commutative rings, e.g. the field of real numbers, relevance logics, linear logics, and substructural logics. In the last case, there is no one-to-one correspondence between the free variables of the defining pair of identities.".
- Absorption_law wikiPageID "286172".
- Absorption_law wikiPageRevisionID "599940951".
- Absorption_law hasPhotoCollection Absorption_law.
- Absorption_law id "p/a010440".
- Absorption_law title "Absorption Law".
- Absorption_law title "Absorption laws".
- Absorption_law urlname "AbsorptionLaw".
- Absorption_law subject Category:Abstract_algebra.
- Absorption_law subject Category:Boolean_algebra.
- Absorption_law subject Category:Lattice_theory.
- Absorption_law subject Category:Theorems_in_propositional_logic.
- Absorption_law type Abstraction100002137.
- Absorption_law type Communication100033020.
- Absorption_law type Message106598915.
- Absorption_law type Proposition106750804.
- Absorption_law type Statement106722453.
- Absorption_law type Theorem106752293.
- Absorption_law type TheoremsInPropositionalLogic.
- Absorption_law comment "In algebra, the absorption law or absorption identity is an identity linking a pair of binary operations.Two binary operations, ¤ and ⁂, are said to be connected by the absorption law if:a ¤ (a ⁂ b) = a ⁂ (a ¤ b) = a.A set equipped with two commutative, associative and idempotent binary operations ("join") and ("meet") that are connected by the absorption law is called a lattice.Examples of lattices include Boolean algebras, the set of sets with union and intersection operators, Heyting algebras, and ordered sets with min and max operations.In classical logic, and in particular Boolean algebra, the operations OR and AND, which are also denoted by and , satisfy the lattice axioms, including the absorption law. ".
- Absorption_law label "Absorption law".
- Absorption_law label "Lei de absorção".
- Absorption_law label "Loi d'absorption".
- Absorption_law label "吸収法則".
- Absorption_law label "吸收律".
- Absorption_law sameAs Loi_d'absorption.
- Absorption_law sameAs 吸収法則.
- Absorption_law sameAs 흡수_법칙.
- Absorption_law sameAs Lei_de_absorção.
- Absorption_law sameAs m.01q110.
- Absorption_law sameAs Q1154428.
- Absorption_law sameAs Q1154428.
- Absorption_law sameAs Absorption_law.
- Absorption_law wasDerivedFrom Absorption_law?oldid=599940951.
- Absorption_law isPrimaryTopicOf Absorption_law.