Definition:Polynomial Ring/Indeterminate

Definition
Let $R$ be a commutative ring with unity.

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

The indeterminate of $\left({S, f, X}\right)$ 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).