Definition:Polynomial over Ring/One Variable
< Definition:Polynomial over Ring(Redirected from Definition:Polynomial over Ring in 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.