Definition:Coefficient of Polynomial

Definition
Let $\left({R, +, \circ}\right)$ be a ring.

Let $\left({S, +, \circ}\right)$ be a subring of $R$.

Let $x \in R$.

Let $\displaystyle f = \sum_{j \mathop = 0}^n \left({a_j \circ x^j}\right) = a_0 + a_1 \circ x + a_2 \circ x^2 + \cdots + a_{n-1} \circ x^{n-1} + a_n \circ x^n$ be a polynomial in $x$ over $R$.

The elements of the set $\left\{{a_0, a_1, \ldots, a_n}\right\}$ are the coefficients of $f$.