Definition:Leading Coefficient of Polynomial

Definition
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 $f$.