Definition:Polynomial Ring/Indeterminate

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

Single indeterminate
Let $(S, f, X)$ be a polynomial ring over $R$.

The indeterminate of $(S, f, X)$ is the term $X$.

Multiple Indeterminates
Let $I$ be a set.

Let $(S, \iota, f)$ be a polynomial ring over $R$ in $I$ indeterminates.

The indeterminates of the polynomial ring are the elements of the image of the family $f$.