Alternative algebra
Algebra where x(xy)=(xx)y and (yx)x=y(xx) / From Wikipedia, the free encyclopedia
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In abstract algebra, an alternative algebra is an algebra in which multiplication need not be associative, only alternative. That is, one must have
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.