# non-associative algebra

A *non-associative algebra* is an algebra^{} in which the assumption of multiplicative associativity is dropped. From this definition, a non-associative algebra does not that the associativity fails. Rather, it enlarges the class of associative algebras, so that any associative algebra is a non-associative algebra.

In much of the literature concerning non-associative algebras, where the meaning of a “non-associative algebra” is clear, the word “non-associative” is dropped for simplicity and clarity.

Lie algebras^{} and Jordan algebras^{} are two famous examples of non-associative algebras that are not associative.

If we substitute the word “algebra” with “ring” in the above paragraphs, then we arrive at the definition of a *non-associative ring*. Alternatively, a non-associative ring is just a non-associative algebra over the integers.

## References

- 1 Richard D. Schafer, An Introduction to Nonassociative Algebras, Dover Publications, (1995).

Title | non-associative algebra |
---|---|

Canonical name | NonassociativeAlgebra |

Date of creation | 2013-03-22 15:06:44 |

Last modified on | 2013-03-22 15:06:44 |

Owner | CWoo (3771) |

Last modified by | CWoo (3771) |

Numerical id | 10 |

Author | CWoo (3771) |

Entry type | Definition |

Classification | msc 17A01 |

Related topic | Semifield |

Related topic | Algebras |

Defines | non-associative ring |