# Definition:Polynomial Ring/Indeterminate

## Definition

Let $R$ be a commutative ring with unity.

#### Single indeterminate

Let $\left({S, \iota, X}\right)$ be a polynomial ring over $R$.

The **indeterminate** of $\left({S, \iota, X}\right)$ is the term $X$.

#### Multiple Indeterminates

Let $I$ be a set.

Let $\left({S, \iota, f}\right)$ be a polynomial ring over $R$ in $I$ **indeterminates**.

The **indeterminates** of $\left({S, \iota, f}\right)$ are the elements of the image of the family $f$.

## Also known as

The **indeterminate(s)** of a polynomial ring are sometimes seen referred to as **variable(s)**.