Definition:Unital Associative Commutative Algebra/Definition 2

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

A unitary algebra over $R$ is an ordered pair $(A, f)$ where:
 * $A$ is a ring with unity
 * $f : R \to A$ is a unital ring homomorphism whose image is contained in the center of $A$

Also see

 * Equivalence of Definitions of Unitary Algebra