Definition:Degree of Polynomial/Zero

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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 if and only if $x$ is a non-zero element of $S$, that is, a constant polynomial.