Definition:Degree of Polynomial/Zero
should be a theorem, not a definition
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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.
Sources
- 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 64$: Remarks $\text{(a)}$
