Definition:Polynomial over Ring/One Variable

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 $P \in R \sqbrk X$ be a polynomial

is a short way of saying:

Let $R \sqbrk X$ be a polynomial ring in one variable over $R$, call its variable $X$, and let $P$ be an element of this ring.

It is of the form:

$\ds \map P x = a_0 + a_1 x + a_2 x^2 + \cdots + a_{n - 1} x^{n - 1} + a_n x^n$

Also see

• Definition:Polynomial over Ring in Multiple Variables

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): polynomial
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): polynomial