Two binary operations, ¤ and ⁂, are said to be connected by the absorption law if:
- a ¤ (a ⁂ b) = a ⁂ (a ¤ b) = a.
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.
- Brian A. Davey; Hilary Ann Priestley (2002). Introduction to Lattices and Order (2nd ed.). Cambridge University Press. ISBN 0-521-78451-4. LCCN 2001043910.
- Hazewinkel, Michiel, ed. (2001) , "Absorption laws", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4
- Weisstein, Eric W. "Absorption Law". MathWorld.
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