Commutator (ring)
In a ring, the commutator of two elements 
and 
, denoted ![$[a,b]$](http://latex.artofproblemsolving.com/8/e/c/8ecbd1ba3da8f2adef66a63f2ab32c47e63fa734.png)
, is the quantity 
. It can be seen as a measure of the failure of the ring to be commutative; in a commutative ring, ![$[a,b]=0$](http://latex.artofproblemsolving.com/1/0/d/10d72a1f32c0ffc7bf1919c3cc45424b39c2009e.png)
. The same definition applies for fields.
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