| Alternative Algebra |
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Information AboutAlternative Algebra |
| CATEGORIES ABOUT ALTERNATIVE ALGEBRA | |
| nonassociative algebra | |
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Equivalently, an algebra is alternative if and only if the Subalgebra generated by any two of its elements is Associative . The equivalence of the two definitions is known as Artin's theorem, after Emil Artin . For any two elements ''x'' and ''y'' in an alternative algebra another simple identity holds: (''xy'')''x'' = ''x''(''yx''). This is called the ''flexible law''. Every Associative Algebra is obviously alternative, but so too are some non-associative algebras such as the Octonion s. The Sedenion s are not alternative. Alternativity in algebras is a condition weaker than associativity but stronger than Power Associativity . |
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