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.
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.
- 1 Richard D. Schafer, An Introduction to Nonassociative Algebras, Dover Publications, (1995).
|Date of creation||2013-03-22 15:06:44|
|Last modified on||2013-03-22 15:06:44|
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