Category:Definitions/Commutative Algebras

This category contains definitions related to Commutative Algebras in the context of Abstract Algebra.
Related results can be found in Category:Commutative Algebras.

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:

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