Noun
English Wikipedia has an article on:anticommutativityWikipedia
anticommutativity (uncountable)
(algebra, physics) The state of being anticommutative.
Due to the anticommutativity of the commutator, the notions of a left and right ideal in a Lie algebra coincide. Source: Internet
If the field's characteristic is not 2 then anticommutativity implies alternativity. Source: Internet