\begin{definition}[Definition:Degree of Polynomial/Ring]
{{questionable|ill-defined}}
Let $\struct {R, +, \circ}$ be a ring.
Let $\struct {S, +, \circ}$ be a subring of $R$.
Let $x \in R$.
Let $\ds P = \sum_{j \mathop = 0}^n \paren {r_j \circ x^j} = r_0 + r_1 \circ x + \cdots + r_n \circ x^n$ be a polynomial in the element $x$ over $S$ such that $r_n \ne 0$.
Then the '''degree of $P$''' is $n$.
The '''degree of $P$''' can be denoted $\map \deg P$ or $\partial P$.
\end{definition}