Associator

In abstract algebra, the term associator is used in different ways as a measure of the nonassociativity of an algebraic structure. Associators are commonly studied as triple systems. In abstract algebra, the term associator is used in different ways as a measure of the nonassociativity of an algebraic structure. Associators are commonly studied as triple systems. For a nonassociative ring or algebra R {displaystyle R} , the associator is the multilinear map [ ⋅ , ⋅ , ⋅ ] : R × R × R → R {displaystyle :R imes R imes R o R} given by Just as the commutator measures the degree of noncommutativity, the associator measures the degree of nonassociativity of R {displaystyle R} .For an associative ring or algebra the associator is identically zero.