Definition:Associative Algebra

Definition
Let $R$ be a commutative ring.

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

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

That is:


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

Also see

 * Definition:Commutative Algebra
 * Definition:Commutative Algebra (Mathematical Branch)