Alternative Algebra

Let A denote an R-algebra, so that A is a vector space over R and


Then A is said to be alternative if, for all x,y in A,


Here, vector multiplication x·y is assumed to be bilinear.

The associator (x,y,z) is an alternating function, and the subalgebra generated by two elements is associative.

See also


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Finch, S. "Zero Divisor Structure in Real Algebras.", R. D. An Introduction to Non-Associative Algebras. New York: Dover, p. 5, 1995.

Referenced on Wolfram|Alpha

Alternative Algebra

Cite this as:

Weisstein, Eric W. "Alternative Algebra." From MathWorld--A Wolfram Web Resource.

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