\begin{definition}[Definition:Degree of Polynomial/Null Polynomial]
Let $\left({R, +, \circ}\right)$ be a ring whose zero is $0_R$.
Let $\left({S, +, \circ}\right)$ be a subring of $R$.
For arbitrary $x \in R$, let $S \left[{x}\right]$ be the set $S \left[{x}\right]$ be the set of polynomials in $x$ over $S$.
The null polynomial $0_R \in S \left[{X}\right]$ does ''not'' have a degree.
\end{definition}