Associativitate

Associativitate^[1] es un lege in algebra.

Associativitate
instantia de: mathematical property[*], rule of replacement[*]

Un operation binari de un magma ${\displaystyle (M;\ast )}$ es associative si e solmente si ${\displaystyle \forall a,b,c\in M\;\;(a\ast b)\ast c=a\ast (b\ast c)}$.

Exemplos

• Le addition de numeros natural: ${\displaystyle (2+7)+4=9+4=13=2+11=2+(7+4)}$.
• Le multiplication de numeros rational: ${\displaystyle ({\tfrac {1}{2}}\cdot {\tfrac {4}{9}})\cdot {\tfrac {3}{2}}={\tfrac {1}{3}}={\tfrac {1}{2}}\cdot ({\tfrac {4}{9}}\cdot {\tfrac {3}{2}})}$.
• Le subtraction de numeros integre non es associative; contraexemplo: ${\displaystyle 3-(6-1)=3-5=-2\neq -4=-3-1=(3-6)-1}$.

Semigruppo

Si un magma es associative, illo se nomina un semigruppo.

Idemassociativitate

Plus debile que le associativitate es le idemassociativitate: ${\displaystyle \forall a\in M\;\;(a\ast a)\ast a=a\ast (a\ast a)}$.

Vide etiam

• Tabella de leges algebric

Referentias

1. Derivation (in ordine alphabetic): (ca) Propietat associativa || (de) Assoziativgesetz || (en) Associative property || (es) Asociatividad (álgebra) || (fr) Associativité || (it) Associatività || (pt) Associatividade || (ro) Asociativitate || (ru) Ассоциативность (математика)