\begin{definition}[Definition:Algebraic Element of Ring Extension]
Let $\struct {R, +, \circ}$ be a commutative ring with unity whose zero is $0_R$ and whose unity is $1_R$.
Let $\struct {D, +, \circ}$ be an integral subdomain of $R$.
Let $x \in R$.
Then $x$ is '''algebraic over $D$''' {{iff}}:
:$\exists \map f x$ over $D$ such that $\map f x = 0_R$
where $\map f x$ is a non-null polynomial in $x$ over $D$.
\end{definition}