Alternative algebra

In abstract algebra, an alternative algebra is an algebra in which multiplication need not be associative, only alternative. That is, one must have

• ${\displaystyle x(xy)=(xx)y}$
• ${\displaystyle (yx)x=y(xx)}$

for all x and y in the algebra.

Every associative algebra is obviously alternative, but so too are some strictly non-associative algebras such as the octonions.