Definition:Polynomial over Ring/One Variable

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Definition

Let $R$ be a commutative ring with unity.


A polynomial over $R$ in one variable is an element of a polynomial ring in one variable over $R$.


Thus:

Let $P \in R \left[{X}\right]$ be a polynomial

is a short way of saying:

Let $R \left[{X}\right]$ be a polynomial ring in one variable over $R$, call its variable $X$, and let $P$ be an element of this ring.


Also see