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... > abstract algebra > algebraic structure > algebra over a field > non-associative algebra > alternative algebra

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alternative algebra

Definition(s)

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.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Alternative_algebra)

Broader concept(s)

non-associative algebra

Narrower concept(s)

In other languages

algèbre alternative

French

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http://data.loterre.fr/ark:/67375/PSR-H2PDWGMD-8

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