Definition:Non-Associative Algebra

Definition

Let $\struct {A_R, \oplus}$ be an algebra over a ring.

Then $\struct {A_R, \oplus}$ is a non-associative algebra if and only if it is not necessarily the case that $\oplus$ is associative.

Also see

• Definition:Non-Associative Ring

• Results about non-associative algebras can be found here.

Sources

• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.26$: Extensions of the Complex Number System. Algebras, Quaternions, and Lagrange's Four Squares Theorem