\begin{definition}[Definition:Degree of Polynomial/Zero]
Let $\struct {R, +, \circ}$ be a ring whose zero is $0_R$.
Let $\struct {S, +, \circ}$ be a subring of $R$.
For arbitrary $x \in R$, let $S \sqbrk x$ be the set of polynomials in $x$ over $S$.
A polynomial $f \in S \sqbrk x$ in $x$ over $S$ is of '''degree zero''' {{iff}} $x$ is a non-zero element of $S$, that is, a constant polynomial.
\end{definition}