Definition:Coefficient of Polynomial/Polynomial Form

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

Let $f = a_1 \mathbf X^{k_1} + \cdots + a_r \mathbf X^{k_r}$ be a polynomial in the indeterminates $\left\{{X_j: j \in J}\right\}$ over $R$.

The ring elements $a_1, \ldots, a_r$ are the coefficients of $f$.