Definition:Constant Polynomial
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Definition
Let $R$ be a commutative ring with unity.
Let $P \in R \left[{x}\right]$ be a polynomial in one variable over $R$.
Definition 1
The polynomial $P$ is a constant polynomial if and only if its coefficients of $x^k$ are zero for $k \ge 1$.
Definition 2
The polynomial $P$ is a constant polynomial if and only if $P$ is either the zero polynomial or has degree $0$.
Definition 3
The polynomial $P$ is a constant polynomial if and only if it is in the image of the canonical embedding $R \to R \left[{x}\right]$.