non-associative algebra

A non-associative algebra is an algebraPlanetmathPlanetmath 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 algebrasMathworldPlanetmath and Jordan algebrasMathworldPlanetmath 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.


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