\begin{definition}[Definition:Monic Polynomial]
Let $R$ be a commutative ring with unity.
Let $f \in R \sqbrk x$ be a polynomial in one variable over $R$.
Then $f$ is '''monic''' {{iff}} $f$ is nonzero and its leading coefficient is $1$.
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Let $\struct {R, +, \circ}$ be a ring with unity whose unity is $1_R$.
Let $\struct {S, +, \circ}$ be a subring of $R$.
Let $\ds f = \sum_{k \mathop = 0}^n a_k \circ x^k$ be a polynomial in $x$ over $S$.
Then $f$ is a '''monic polynomial''' {{iff}} its leading coefficient $a_n$ is $1_R$.
\end{definition}