Definition:Associative Algebra

Definition
Let $R$ be a commutative ring.

Let $\struct {A_R, *}$ be an algebra over $R$.

Then $\struct {A_R, *}$ is an associative algebra $*$ is an associative operation.

That is:


 * $\forall a, b, c \in A_R: \paren {a * b} * c = a * \paren {b * c}$

Also see

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