Definition:Coefficient of Polynomial

Definition
Let $A$ 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 $\{X_j : j \in J \}$ over $A$.

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