\begin{definition}[Definition:Canonical Homomorphism from Ring to Unital Algebra]
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 $a \cdot 1$.
\end{definition}