# 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.

## Words

This table shows the example usage of word lists for keywords extraction from the text above.

Word | Word Frequency | Number of Articles | Relevance |
---|---|---|---|

x | 11 | 29892 | 0.709 |

algebra | 6 | 3174 | 0.553 |

y | 7 | 24981 | 0.467 |

alternative | 5 | 30646 | 0.321 |