Definition:Commutative Algebra (Abstract 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 a commutative algebra $\oplus$ is a commutative operation.

That is:


 * $\forall a, b \in A_R: a \oplus b = b \oplus a$

Also see

 * Definition:Associative Algebra