Commutator (ring)
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In a ring, the commutator of two elements 
and 
, denoted ![[a,b]](http://alt1.artofproblemsolving.com/Forum/latexrender/pictures/1/4/7/1475c39442659c6febe03b2e1809dbde6ec5fb5a.gif)
, 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://alt1.artofproblemsolving.com/Forum/latexrender/pictures/2/d/7/2d7be61142ddb676a1720e0b610e243b5d8ebbbe.gif)
. The same definition applies for fields.
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