Definition:Leading Coefficient of Polynomial

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

Let $f = a_0 + a_1 X + \cdots + a_{r-1} X^{r-1} + a_r X^r$ be a polynomial in the single indeterminate $X$ over $A$.

Then the ring element $a_r$ is called the leading coefficient of $f$.