Algebra over a commutative ring
= Algebra over a commutative ring
= Algebra over a ring
{synonym}
An algebra over a <commutative ring> $R$ is a <ring> $A$ with a specified unital <ring homomorphism> $R\to A$ whose image commutes with every element of $A$. Scalar multiplication is $r\cdot a=\varphi(r)a$. For commutative $A$, the commutation requirement is automatic.