Definition:Commutative Algebra

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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 if and only if $\oplus$ 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