Definition:Commutative Algebra

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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 if and only if $\oplus$ is a commutative operation.

That is:

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


Also see


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