In Lie algebras this identity is replaced with the Jacobi identity.
Alternative algebras do not possess this property, and instead possess their weaker namesake property which is stronger than the "power" kind of this property. In Lie algebras this identity is replaced with the Jacobi identity. A magma which has this property is called a semigroup. This adjective is prefixed by the words "set" or "fully" when describing caches which are not direct-mapped. The abstract data type known as this kind of array is also called a (*) dictionary and can be implemented with a hash table. This property holds of the quaternions but not of octonions. For ten points, name this mathematical property of binary operations that says that parentheses can be moved around without changing the value of an expression, often contrasted with the commutative property.
Alternative algebras do not possess this property, and instead possess their weaker namesake property which is stronger than the "power" kind of this property.
associative property or identity or associativity