What is "alternative algebra"

n. (context algebra English) An algebra such that every subalgebra generated by two elements is associative.

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

• x(xy) = (xx)y
• (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. The sedenions, on the other hand, are not alternative.