Definition:Associative Algebra

Definition

Let $\left({A_R, \oplus}\right)$ be an algebra over a ring.

Then $\left({A_R, \oplus}\right)$ is an associative algebra iff $\oplus$ is associative.

That is:

$\forall a, b, c \in A_R: \left({a \oplus b}\right) \oplus c = a \oplus \left({b \oplus c}\right)$

Sources

• John C. Baez: The Octonions (2002): 1.1 Preliminaries