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Copyright © 2019 American Chemical Society.About a decade ago, it was realised that the satisfaction of a given identity (or equation) of the form f ( x 1 , … , x n ) ≈ f ( y 1 , … , y n ) in an algebra is equivalent to the algebra forcing a loop into any graph on which it acts and which contains a certain finite subgraph associated with the identity. Such identities have since also been called loop conditions, and this characterisation has produced spectacular results in universal algebra, such as the satisfaction of a Siggers identity s ( x , y
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