\begin{definition}[Definition:Degree of Polynomial/Integral Domain]
Let $\struct {R, +, \circ}$ be a commutative ring with unity whose zero is $0_R$.
Let $\struct {D, +, \circ}$ be an integral subdomain of $R$.
Let $X \in R$ be transcendental over $D$.
Let $\ds f = \sum_{j \mathop = 0}^n \paren {r_j \circ X^j} = r_0 + r_1 X + \cdots + r_n X^n$ be a polynomial over $D$ in $X$ such that $r_n \ne 0$.
Then the '''degree of $f$''' is $n$.
The '''degree of $f$''' is denoted on {{ProofWiki}} by $\map \deg f$.
\end{definition}