Definition:Unital Associative Commutative Algebra/Definition 2

Definition
Let $R$ be a commutative ring with unity.

A unital associative commutative algebra over $R$ is a ring under $A$, that is, an ordered pair $(A, f)$ where:
 * $A$ is a commutative ring with unity
 * $f : R \to A$ is a unital ring homomorphism

Also see

 * Equivalence of Definitions of Unital Associative Commutative Algebra