- Associator
In
abstract algebra , for a ring or algebra , the associator is themultilinear map given by:
Just like the
commutator measures the degree of noncommutativity, the associator measures the degree of nonassociativity of anonassociative ring or algebra. It is identically zero for anassociative ring or algebra.The associator in any ring obeys the identity
:
The associator is alternating precisely when is an
alternative ring .In
higher-dimensional algebra , where there may be non-identity morphisms between algebraic expressions, an associator is an isomorphism:
See also
*
commutator
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