Associativitate

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

Associativitate es un lege in algebra.

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

Exemplos

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

Semigruppo

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

Idemassociativitate

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

Vide etiam

• Tabella de leges algebric