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# Associator

In abstract algebra, for a nonassociative ring R, the associator is the multilinear map

$[\cdot,\cdot,\cdot] : R \times R \times R \to R : (x, y, z) \mapsto [x,y,z] := (xy)z - x(yz).$

The associater measures the degree of nonassociativity of a ring and is zero for associative rings .