Definition:Commutative Algebra

Definition
Let $R$ be a commutative ring.

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

Then $\struct {A_R, \oplus}$ is a commutative algebra $\oplus$ is a commutative operation.

That is:


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

Also known as
Some sources suggest that commutative algebra can be considered as a branch of algebraic geometry.

Also see

 * Definition:Associative Algebra