Definition:Leading Coefficient of Polynomial

Definition
Let $R$ be a commutative ring with unity.

Let $P \in R[X]$ 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 $P$.

Let $\left({R, +, \circ}\right)$ be a ring.

Let $\left({S, +, \circ}\right)$ be a subring of $R$.

Let $\displaystyle f = \sum_{k \mathop = 0}^n a_k \circ x^k$ be a polynomial in $x$ over $S$.

The coefficient $a_n \ne 0_R$ is called the leading coefficient of $f$.

Also see

 * Definition:Degree of Polynomial