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.
== Ring theory ==
For a nonassociative ring or algebra
R
{\displaystyle R}
, the associator is the multilinear map
[
⋅
,
⋅
,
⋅
]
:
R
×
R
×
R
→
R
{\displaystyle [\cdot ,\cdot ,\cdot ]:R\times R\times R\to R}
given by...