\begin{definition}[Definition:Ring of Polynomials in Ring Element]
Let $\struct {R, +, \circ}$ be a commutative ring.
Let $\struct {D, +, \circ}$ be an integral subdomain of $R$.
Let $x \in R$.
The subring of $R$ consisting of all the polynomials in $x$ over $D$ is called the '''ring of polynomials over $D$''' and is denoted $D \sqbrk x$.
\end{definition}