\begin{definition}[Definition:Leading Coefficient of Polynomial]
Let $R$ be a commutative ring with unity.
Let $P \in R \sqbrk X$ be a nonzero polynomial over $R$.
Let $n$ be the degree of $P$.
The '''leading coefficient''' of $P$ is the coefficient of $x^n$ in $P$.
{{questionable|the below is ill-defined}}
Let $\struct {R, +, \circ}$ be a ring.
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 $S$.
The coefficient $a_n \ne 0_R$ is called the '''leading coefficient''' of $f$.
\end{definition}