Definition:Absorption Law
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Definition
Let $\struct {S, \circ, *}$ be an algebraic structure.
Let both $\circ$ and $*$ be commutative.
Then $\circ$ absorbs $*$ if and only if:
- $\forall a, b \in S: a \circ \paren {a * b} = a$
This equality is called the absorption law of $\circ$ for $*$.
Also see
- Results about absorption laws can be found here.
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {III}$: The Natural Numbers: $\S 14$: Orderings: Exercise $14.23 \ \text {(a)}$