Definition:Degree of Polynomial/Zero

Definition

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 $S$.

A polynomial $f \in S \left[{x}\right]$ in $x$ over $S$ is of degree zero if and only if $x$ is a non-zero element of $S$, that is, a constant polynomial.