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Alternativity
In abstract algebra, a magma G is said to be left alternative if (xx)y=x(xy) for all x and y in G and right alternative if y(xx)=(yx)x for all x and y in G. A magma that is both left and right alternative is said to be alternative.
Any associative magma (semigroup) is clearly alternative. More generally, a magma in which every pair of elements generates an associative submagma must be alternative. The converse, however, is not true, in contrast to the situation in alternative algebras. In fact, an alternative magma need not even be power-associative.
10-26-2009 08:16:03
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details