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minor things

1) There is no need to introduce notation F for the field. Simply say
Let $A$ be a not-necessarily associative algebra over a field.
Let $A$ be a not-necessarily associative algebra.

2) 'An associator' implies that there are many associators. This
is not in line with the definition. What about:

The mapping $ [\ , , ] \colon A\times A\times A \to A$ given by
[a,b,c]=(ab)c-a(bc),\quad a,b,c\in A
is the \emph{associator} in $A$.

3) Consider:
'$ [ , , ]$ is trivial' -> '$ [\ , , ]$ is identically zero'
or 'the associator vanishes identically'

This is more precice.

4) Add 'Commutator' to see also list.

5) A reference would be great... Where are these used?

Parting words from the person who closed the correction: 
Status: Accepted
Reference to the user who closed the correction.: 
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