# 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 $f$.

- 2000: Pierre A. Grillet:
*Abstract Algebra*: $\S \text{III}.6$