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 x ( x y ) = ( x x ) y {\displaystyle x(xy)=(xx)y} ( y x ) x = y ( x x ) {\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.


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