Alternativity should not be confused with Alternatization.
In abstract algebra, alternativity is a property of a binary operation. A magma G is said to be if
(xx)y=x(xy)
x,y\inG
y(xx)=(yx)x
x,y\inG.
Any associative magma (that is, a semigroup) is alternative. More generally, a magma in which every pair of elements generates an associative submagma must be alternative. The converse, however, is not true, in contrast to the situation in alternative algebras. In fact, an alternative magma need not even be power-associative: already the expression
(xx)(xx)
(x(x(xx)))