Definition:Canonical Homomorphism from Ring to Unital Algebra

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

Let $B$ be an unital algebra over $A$ with unit $1$ whose underlying module is unitary.

The canonical homomorphism $A \to B$ is the algebra homomorphism that sends $a \in A$ to $a \cdot 1$.

Also see

 * Canonical Homomorphism to Unital Associative Algebra is Homomorphism to Underlying Ring