Category:Commutative Algebras

This category contains results about Commutative Algebras in the context of Abstract Algebra.
Definitions specific to this category can be found in Definitions/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:

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