non-associative algebra (original) (raw)

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).