\begin{definition}[Definition:Algebra Defined by Ring Homomorphism]
Let $R$ be a commutative ring.
Let $\struct {S, +, *}$ be a ring.
Let $f : R \to S$ be a ring homomorphism.
Let the image of $f$ be a subset of the center of $S$.
Let $S_R$ be the module defined by the ring homomorphism $f$.
The '''algebra defined by $f$''' is the algebra over $R$ defined as:
:$\struct {S_R, *}$
\end{definition}